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System of equations

Solution of a system of equations

Solve this system of equations

What is the solution to this system of…

Set of two or more equations that contain two or more variabl…

Set of (x,y) values that make all equations in a system true.

3x + 2y = - 12... x + y = - 5

System of equations

Set of two or more equations that contain two or more variabl…

Solution of a system of equations

Set of (x,y) values that make all equations in a system true.

system of equations

Solving systems of equations

substitution method

elimination method

A system of equations is a collection of two or more equation…

In solving a system of equations, we try to find values for e…

The method of solving "by substitution" works by solving one…

The elimination method is where you actually eliminate one of…

system of equations

A system of equations is a collection of two or more equation…

Solving systems of equations

In solving a system of equations, we try to find values for e…

Standard Form

Slope-Intercept Form

feasible points

linear inequality

The standard form of a linear equation is Ax + By = C, where…

The slope-intercept form of a linear equation is y = mx + b,…

The set of all solutions that satisfy an equation, and inequa…

A mathematical sentence, such as Ax + By + C < Dx + Ex + F, w…

Standard Form

The standard form of a linear equation is Ax + By = C, where…

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b,…

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pa…

a system of linear equations that has an infinite number of s…

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pair that satisfies bot…

consistent

a system of linear equations that has at least one ordered pa…

dependent

a system of linear equations that has an infinite number of s…

consistent

dependent

elimination method

inconsistent

system of equations that has at least one solution; could be…

a system that is consistent and has infinitely many solutions…

one way to solve a system algebraically

a system that has no solution; parallel lines

consistent

system of equations that has at least one solution; could be…

dependent

a system that is consistent and has infinitely many solutions…

consistent

dependent

elimination method

inconsistent

A system of equations that has at least one solution

A consistent system that has infinitely many solutions.

If a=b and c=d, then a+c=b+d and a-c=b-d. In this method, you…

A system of equations that has no solution.

consistent

A system of equations that has at least one solution

dependent

A consistent system that has infinitely many solutions.

system of linear equations

solution of a system of linear equations

substitution method

elimination method

A set of two or more linear equations containing two or more…

Any ordered pair that satisfies all the equations in the syst…

A method used to solve systems of equations by solving an equ…

A method used to solve systems of equations in which one vari…

system of linear equations

A set of two or more linear equations containing two or more…

solution of a system of linear equations

Any ordered pair that satisfies all the equations in the syst…

system of linear equations

solution of a system of linear equations

substitution method

elimination method

A set of two or more linear equations containing two or more…

Any ordered pair that satisfies all the equations in the syst…

A method used to solve systems of equations by solving an equ…

A method used to solve systems of equations in which one vari…

system of linear equations

A set of two or more linear equations containing two or more…

solution of a system of linear equations

Any ordered pair that satisfies all the equations in the syst…

system of linear equations

solution of a linear equation

consistent independent system

inconsistent system

a linear system that consists of two or more linear equations…

an ordered pair that satisfies each equation in the system

a linear line that has exactly one solution and the lines int…

a linear system with no solution and the lines are parallel

system of linear equations

a linear system that consists of two or more linear equations…

solution of a linear equation

an ordered pair that satisfies each equation in the system

200

2

-3

-4

Miranda wants to open a sandwich shop. Her initial supplies w…

Mark-Anthony wants to start selling phones in the mall. His i…

Solve for the x value in the system... y = x - 1... y = 2x + 2

Solve for the y value in the system... y = x - 1... y = 2x + 2

200

Miranda wants to open a sandwich shop. Her initial supplies w…

2

Mark-Anthony wants to start selling phones in the mall. His i…

System of Equations

Consistent

Independent

Dependent

Two equations with the same variables.

A system of equations that has at least one ordered pair to s…

A system of equations that has only one solution.

A system of equations that has many solutions.

System of Equations

Two equations with the same variables.

Consistent

A system of equations that has at least one ordered pair to s…

Consistent

Dependent

Elimination Method

Inconsistent

a system of equations that has at least one ordered pair that…

a system of equations that has an infinite number of solutions

solving systems by adding or subtracting equations to elimina…

A system of equations that has no solutions

Consistent

a system of equations that has at least one ordered pair that…

Dependent

a system of equations that has an infinite number of solutions

System of Linear Equations

Soultion of a System of Linear Equations

Substitution

Elimination

Two or more equations with two or more variables

Any ordered pairs that satisfies the system's equations

A method to reduce two equations to one equation that has one…

A method to elimate a variable to make one equation

System of Linear Equations

Two or more equations with two or more variables

Soultion of a System of Linear Equations

Any ordered pairs that satisfies the system's equations

Consistent and independent

Consistent and dependent

Inconsistent

Substitution

Different slope and different Y intercept

Same slope same Y intercept

Same slope different Y intercept

Solve one equation for one of the variables and plug into oth…

Consistent and independent

Different slope and different Y intercept

Consistent and dependent

Same slope same Y intercept

Consistent

Dependent

Elimination Method

Inconsistent

A system of equations that has at least one solution; could b…

A system that is consistent and has infinitely many solutions…

Solving a system by narrowing it down to one variable first

A system that has no solution; parallel lines

Consistent

A system of equations that has at least one solution; could b…

Dependent

A system that is consistent and has infinitely many solutions…

when you find a solution to a system o…

What are the three methods for solving…

What are the three possible types of s…

When graphing a linear inequality you…

The point of intersection

Graphing, substitution, elimination

One solution, no solution, infinitely many solutions

Shade a region

when you find a solution to a system o…

The point of intersection

What are the three methods for solving…

Graphing, substitution, elimination

consistent system

dependent system

inconsistent system

independent system

a system of equations or inequalities that has at least one s…

a system of equations that has infinitely many solutions

a system of equations or inequalities that has no solution

a system of equations that has exactly one solution

consistent system

a system of equations or inequalities that has at least one s…

dependent system

a system of equations that has infinitely many solutions

consistent

dependent

elimination

inconsistent

a system of equations that has at least one ordered pair that…

a system of equations that has an infinite number of solutions

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pair that satisfy both…

consistent

a system of equations that has at least one ordered pair that…

dependent

a system of equations that has an infinite number of solutions

Define solution to a system of linear…

How can you know that a given ordered…

Explain how to solve a system of linea…

Explain how to solve a system of linea…

A solution to a system of linear equations is an input that p…

If an ordered pair is a solution to a system then it will mak…

If needed rewrite the equations in slope intercept form. Firs…

If needed rewrite the equations so that at least one variable…

Define solution to a system of linear…

A solution to a system of linear equations is an input that p…

How can you know that a given ordered…

If an ordered pair is a solution to a system then it will mak…

system of linear equations

solution of a system of linear equations

substitution method

elimination method

A set of two or more linear equations containing two or more…

Any ordered pair that satisfies all the equations in the syst…

A method used to solve systems of equations by solving an equ…

A method used to solve systems of equations in which one vari…

system of linear equations

A set of two or more linear equations containing two or more…

solution of a system of linear equations

Any ordered pair that satisfies all the equations in the syst…

consistent

inconsistent

independent

dependent

System has at least one solution (intersecting or same line)

System has no solutions (parallel lines)

System has exactly one solution (intersecting)

System has an infinite number of solutions (same line)

consistent

System has at least one solution (intersecting or same line)

inconsistent

System has no solutions (parallel lines)

system of linear equations

solution to a two variable linear system

approximate solution

substitution method for solving a system

Two equations in two variables; a set of collection of equati…

An ordered pair of numbers that is a solution to each equatio…

A reasonable estimate for a point of intersection. A rounded…

A method used to solve a system of equations in which variabl…

system of linear equations

Two equations in two variables; a set of collection of equati…

solution to a two variable linear system

An ordered pair of numbers that is a solution to each equatio…

Solve: 2x+7y=14... 4x+14y=21

Solve: 4x+2y+3z=1 ... 2x-3y+5z=-14... 6x-y…

A florist must make 5 identical brides…

You have $25 to spend on 21 pounds of…

No Solution (parallel lines)

Solution (2, 1, -3)

2.5x + 4y + 2z = 32... x + y + z = 12... x = 2(y + z)

1.4x + 1.1y + 1.3z = 25... x + y + z = 21... y = 2(x + z)

Solve: 2x+7y=14... 4x+14y=21

No Solution (parallel lines)

Solve: 4x+2y+3z=1 ... 2x-3y+5z=-14... 6x-y…

Solution (2, 1, -3)

system of equations

solution

consistent system

inconsistent system

more than one line

point of intersection of 2 (or more) lines

- 1 solution (point of intersection)... - lines have different s…

- no solution (point of intersection)... - lines are parallel/sl…

system of equations

more than one line

solution

point of intersection of 2 (or more) lines

consistent

dependent

elimination method

inconsistent

A system of equations that has at least one solution

A consistent system that has infinitely many solutions

If a=b and c=d, then a+c=b+d and a-c=b-d. In this method, you…

A system of equations that has no solution

consistent

A system of equations that has at least one solution

dependent

A consistent system that has infinitely many solutions

System of Linear Equations

Solution of a system of linear equations

Substitution Method

Elimination Method

two or more linear equations

The ordered pair that makes all the equations in a system true

When you solve one of the equations in the system for x or y,…

When you add or subtract the linear equations so that one var…

System of Linear Equations

two or more linear equations

Solution of a system of linear equations

The ordered pair that makes all the equations in a system true

System of equations

Common solution

supply

demand

Two or more equations with the same set of variables that you…

In a system of linear equations, a solution that is true for…

How much there is of a product

How much of a product people want

System of equations

Two or more equations with the same set of variables that you…

Common solution

In a system of linear equations, a solution that is true for…

system of linear equations

solution of a system

consistent

independent

Two or more linear equations using the same variables.

Any ordered pair that makes all of the equations in a system…

uniform

The experimental factor that is manipulated; the variable who…

system of linear equations

Two or more linear equations using the same variables.

solution of a system

Any ordered pair that makes all of the equations in a system…

Variable

Constants

coefficient

Dependent variable

4x-7=5 x is the variable (unknown)... Typically, we use a sing…

4x-7=5 7 and 5 are constants neither number changes (stays th…

4x-7=5 4 is the coefficient... number or symbol multiplied with…

y=mx+b y is the dependent dependent depends on what independent

Variable

4x-7=5 x is the variable (unknown)... Typically, we use a sing…

Constants

4x-7=5 7 and 5 are constants neither number changes (stays th…

System

Solution

System

Solution

Two or more linear equations that use the same variables

the ordered pair that makes both equations true at the same t…

Two or more linear inequalities that use the same variables

Set of ordered pairs that make both inequalities true at the…

System

Two or more linear equations that use the same variables

Solution

the ordered pair that makes both equations true at the same t…

system of linear equations

solution of a system of linear equations

substitution method

elimination method

A set of two or more linear equations containing two or more…

Any ordered pair that satisfies all the equations in the syst…

A method used to solve systems of equations by solving an equ…

A method used to solve systems of equations in which one vari…

system of linear equations

A set of two or more linear equations containing two or more…

solution of a system of linear equations

Any ordered pair that satisfies all the equations in the syst…

coinciding lines

elimination

feasible region

intersection

two lines that lie on top of one another

the process of eliminating one of the variables in a system o…

the area defined by a set of coordinates that satisfy a syste…

the point where two lines meet

coinciding lines

two lines that lie on top of one another

elimination

the process of eliminating one of the variables in a system o…

Linear programming

Constraints

Convex polygon

Feasible region

A process that utilizes a system of inequalities which determ…

Inequalities that define a region

Shape formed by the boundaries

The area of intersection

Linear programming

A process that utilizes a system of inequalities which determ…

Constraints

Inequalities that define a region

consistent

dependent

elimination method

inconsistent

system of equations that has at least one solution; could be…

a system that is consistent and has infinitely many solutions…

one way to solve a system algebraically

a system that has no solution; parallel lines

consistent

system of equations that has at least one solution; could be…

dependent

a system that is consistent and has infinitely many solutions…

Dependent system

Independent system

Consistent system

Inconsistent system

System with infinte solutions

System with one solution

System with at least 1 solution

System with no solutions

Dependent system

System with infinte solutions

Independent system

System with one solution

Systems of Equations

Consistent

Inconsistent

Independent

a set of equations used to find the values of the variables "…

one solution.

no solution.

ONLY one solution.

Systems of Equations

a set of equations used to find the values of the variables "…

Consistent

one solution.

break-even point

system of equations

consistent

inconsistent

The point at which the income equals the cost.

A set of equations with the same variables.

A system of equations that has at least one ordered pair that…

A system of equations with no ordered pair that satisfy both…

break-even point

The point at which the income equals the cost.

system of equations

A set of equations with the same variables.

break-even point

consistent

inconsistent

independent

point at which income equals cost

system with at least one solution

system with no solutions

system with exactly one solution

break-even point

point at which income equals cost

consistent

system with at least one solution

Systems of linear Equations

Solution of a system of linear equations

No solution

Infinitely many solutions

Two or more linear equations using the variable

Any ordered pair in a system that makes all the equations of…

When the graphs of the equation in a system are parallel with…

The number of solutions of a system of equations in which the…

Systems of linear Equations

Two or more linear equations using the variable

Solution of a system of linear equations

Any ordered pair in a system that makes all the equations of…

Consistent system

Inconsistent system

Independent system

Dependent system

A system of equations is a ____ if it has at least one solution

A system of equation with no solution is called

A system of linear equations with exactly one solution is cal…

A system of linear equations with an infinite number of solut…

Consistent system

A system of equations is a ____ if it has at least one solution

Inconsistent system

A system of equation with no solution is called

system of linear equations

solution

consistent systems

inconsistent systems

a set of two or more linear equations containing two or more…

If an ordered pair is a ________, it will make both equations…

systems with at least one solution

systems with no solution

system of linear equations

a set of two or more linear equations containing two or more…

solution

If an ordered pair is a ________, it will make both equations…

when shading an inequality, when shoul…

if the lines are the same, there are _…

if the lines never cross, (parallel) t…

if the lines intersect, there is ___ s…

⬇️. ⬆️... < <. >. >... _. _

many

no

one

when shading an inequality, when shoul…

⬇️. ⬆️... < <. >. >... _. _

if the lines are the same, there are _…

many

system of linear equations

solution of a system of linear equations

substitution method

elimination method

A set of two or more linear equations containing two or more…

Any ordered pair that satisfies all the equations in the syst…

A method used to solve systems of equations by solving an equ…

A method used to solve systems of equations in which one vari…

system of linear equations

A set of two or more linear equations containing two or more…

solution of a system of linear equations

Any ordered pair that satisfies all the equations in the syst…

if a system of two linear equations ha…

if a system of two linear equations ha…

if a system of two linear equations ha…

if a system of two linear equations ha…

they have different slopes

they have same or different intercepts

it's not zero

they have the same slope

if a system of two linear equations ha…

they have different slopes

if a system of two linear equations ha…

they have same or different intercepts

Equation

Inequality

Number Line Graph

Ordered pair

A mathematical sentence that contains an equals sign.

A mathematical sentence that contains less than, greater than…

Graphing of integers

A pair of numbers that give the location of a point on a x an…

Equation

A mathematical sentence that contains an equals sign.

Inequality

A mathematical sentence that contains less than, greater than…

system of linear equations

substitution method

elimination method

consistent system

A set of two or more linear equations containing two or more…

A method used to solve systems of equations by solving an equ…

A method used to solve systems of equations in which one vari…

A system of equations or inequalities that has at least one s…

system of linear equations

A set of two or more linear equations containing two or more…

substitution method

A method used to solve systems of equations by solving an equ…