Solve the System of Equations with Elimination

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

To eliminate a variable in the system, should you add the equations or subtract the equations?

• Add

• Subtract

• Neither

Answer explanation

We want to add the equations together in order to eliminate one of the variables. We have opposite terms (3x and -3x) that will "cancel/zero out" (be eliminated) when we add the equations together.

Which variable would be easiest to eliminate?

• x

• y

• Neither

Answer explanation

The terms with x in them have opposite coefficients (4x and -4x), so they will be the easiest to eliminate when we add the equations together.

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Answer explanation

The lines intersect at (1,3) so that is the solution.

7x - y = 10

-7x + y = -14

• No Solution

• (4, 1)

• Infinitely Many Solutions

• (2, -4)

Answer explanation

7x - y = 10

-7x + y = -14

All of the like terms have opposite coefficients, so both variables will be eliminated when we add the equations together. We cannot eliminate one without the other.

We are left with:

0=-4

This is a contradiction (false), so there is NO SOLUTION.

Solve by elimination
-12x-10y= 0
6x+5y= -1

• infinite solutions

• (0,0)

• no solution

• (2,1)

Solve the system:

2x+3y=1

-x+y= -3

Write the solution to this system of equations as a coordinate pair (x,y) with no spaces.

3x + y = 10

-x - y = -20

Write the solution to this system of equations as a coordinate pair, (x,y) with no spaces

7x + 2y = -5

-7x + 5y = 12

What variable do you eliminate?

4x + 8y = 20

−4x + 2y = −30

• X because they have opposite signs

• Y because they have opposite signs