6-1 Solving Systems by Graphing. 6-2 Solving Systems by Substitution. 6-3 Solving Systems by Elimination. 6-4 Solving Special Systems. 6-5 Applying Systems. 6-6 Solving Linear Inequalities. 6-7 Solving Systems of Linear Inequalities.
Terms in this set (...)
system of linear equations
A set of two or more linear equations containing two or more variables.
2x + 3y = −1 x − 3y = 4
solution of a system of linear equations
Any ordered pair that satisfies all the equations in the system.
x + y = −1 −x + y = −3 Solution: (1, −2)
A method used to solve systems of equations by solving an equation for one variable and substituting the resulting expression into the other equation(s).
y = 2x y = x + 5
<b>Step 1</b> y = 2x y = x + 5
<b>Step 2</b> <color blue>y</color> = x + 5 <color blue>2x</color> = x + 5
Step 3 2x <color red>− x</color> = x <color red>− x</color> + 5 x = <color green>5</color>
Step 4 y = 2<color green>x</color> y = 2<color green>(5)</color> y = <color purple>10</color>
USE WHEN... • Both equations have the same variable with the same or opposite coefficients. • A variable term in one equation is a multiple of the corresponding variable term in the other equation.
EXAMPLE 3x + 2y = 8 5x + 2y = 12
or 6x + 5y = 10 3x + 2y = 15
A system of equations or inequalities that has at least one solution.
x + y = 6 x − y = 4 Solution: (5, 1)
A system of equations or inequalities that has no solution.
A system of equations that has exactly one solution.
x + y = 7 x − y = 1 Solution: (4, 3)
A system of equation that has infinitely many solutions.
x + y = 2 2x + 2 y = 4
An inequality that can be written in one of the following forms: <i>ax < b</i>, <i>ax > b</i>, <i>ax ≤ b</i>, <i>ax ≥ b</i>, or <i>ax ≠ b</i>, where <i>a</i> and <i>b</i> are constants and <i>a</i> ≠ 0.
solution of a linear inequality
An ordered pair or ordered pairs that make the inequality true.
Inequality: 3x + 2y ≥ 6
system of linear inequalities
A set of two or more linear inequalities containing two or more variables.
2x + 3y > −1 x − 3y ≤ 4
solution of a system of inequalities in two variables
Any ordered pair that satisfies all the inequalities in the system.