Elimination Method in Linear Systems

To eliminate one variable

To factor the equations

To graph the equations

To find the slope

When the equations are already equal

When the variables are different

When the coefficients are the same

When the coefficients are not the same or opposite

A coefficient of a variable

A number that stays the same

A term with a variable

A variable that changes

x + y = 0 and 2x - y = 5

x - y = 1 and 2x + 3y = 4

2x + 10y = 2 and 3x - 5y = -17

4x + 3y = 7 and 5x - 2y = 8

To change the constant term

To make the coefficients of y equal

To make the coefficients of x equal

To simplify the equation

2x = -8

6x = 12

8x = -32

4x = 16

x = -8

x = 8

x = -4

x = 4

Graph the solution

Check the solution by substitution

Substitute x = -4 into one of the original equations

Solve for y using the same equation

(-4, 0)

(4, 1)

(-4, 1)

(4, -1)

To eliminate a variable

To simplify the equation

To factor the equation

To find the slope