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Linear Systems
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Ch 11/12 Vocab
Key Concepts:
Terms in this set (17)
Graphing Method
A process of solving a system of equations by graphing both equations and determining the intersection point.
Linear Combination Method
A process of solving a system of equations by adding two equations together, resulting in an equation with one variable.
Substitution Method
A process of solving a system of equations by substituting a variable in one equation with an equivalent expression.
System of Equations
A set of two or more equations containing a between two or more quantities
Break-Even Point
The point when the income and expenses are equal. Also known as the solution or intersection point.
One Solution
When each equation in the system have different slopes (or intersect once).
No Solution
When the equations have the same slope but different y-intercepts. Also, a system of equations in which there are no intersection points. (the lines are parallel)
Infinitely Many Solutions
When the equations have the same slope and the same y-intercept. A system of equations in which all values on the line are true (the equations are the same line).
Ordered Pair
Solutions to systems of equations should always be written as an ___________ ___________.
(2,2)
What is the solution to the system?
(4,-4)
What is the solution to the system?
(-1,-1)
What is the solution to the system?
No Solution
y = 2x + 5
y = 2x - 7
Infinitely Many Solutions
y = -4x + 2
4x + y = 2
One Solution
different coefficient term and constant
Infinitely Many Solutions
same coefficient term and constant
No Solution
same coefficient term and different constant
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