7.4 Systems of Equations by Elimination - Multiply one & both

7.4 Elimination by Multiplication

Multiple Select

What is a solution to a system of linear equations?

• The point where both lines intersect

• The point where the y-axis and x-axis meet

• An ordered pair that both lines share

• A salt dissolved in water

​If I tried to add these two equations up, would anything eliminate?

Open Ended

Why wouldn't anything eliminate?

​Our added step - Multiply one of the equations to make numbers similar.

​Here is where we are now -

​Then solve as normal!

​Lets try another

​Lets try one - find x and y

Multiple Choice

To add and eliminate the x’s to solve, what value should you multiply the top equation by.

2x - 5y = 10.

4x + 15y = -10

• -2

• 2

• 3

• -3

Multiple Choice

what do you need to multiply the top equation by in order to add the two equations up?

5x - 2y = 11

-10x + 3y = -4

• 5

• -1

• 2

• -2

​Steps to solve these




1. multiply the equation to get similar numbers
2. Add equations to find x or y
3. Plug x or y back into the equation.

​Lets try another - find x and y

Multiple Choice

Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8 

• (5, 8)
• (5, -8)
• (-5, -18)
• (-5, 8)

Multiple Choice

Solve by elimination.

6x - y = 2

-3x - 6y = 12

• (2,0)

• no solution

• (0,-2)

• infinite solutions

Multiple Choice

Solve the system using elimination.

2x + 3y = 6

x + 2y = 5

• ( 4 , -3 )

• ( -3 , 4 )

• ( 3 , 4 )

• ( 4 , 3 )

Multiple Choice

Solve the following system by using elimination:

-2x - 5y = -15

x + 8y = 13

• (5, 1)

• (5, -1)

• (-5, 1)

​7.4 Elimination by Multiplying Part Two

If I tried to multiply one of these equations to get a similar number, there would be a problem.

If I tried to multiply one of these equations to get a similar number, there would be a problem.

Open Ended

What is the issue?

If I tried to multiply one of these equations to get a similar number, there would be a problem.

​I will do another

Multiple Choice

Out of the options below, what would you multiply both equations by to eliminate the x-values?

• Multiply the top equation by 6 and the bottom equation by -4

• Multiply the top equation by 6 and the bottom equation by 4

• Multiply the top equation by 2 only

• Multiply the top equation by 4 and the bottom equation by -6

Multiple Choice

Spongebob decided he's going to multiply the top equation by 6 and the bottom equation by -4 to create opposites. Select the new equations for Spongebob.

• -24x + 60y = 84

  24x - 36y = -60

• -24x + 60y = 14

  24x - 36y = -60

• -24x + 60y = 84

  24x - 36y = 15

• -24x + 60y = 84

  24x + 9y = 15

Multiple Choice

Elmo decided he's going to multiply the top equation by 2 and the bottom equation by 3 to create opposites. Select the new equations for Elmo.

• 6x - 18y = 18

  -6x + 24y = -6

• 6x - 18y = 9

  -6x + 24y = -6

• 6x - 18y = 18

  -6x + 24y = -2

• 6x - 18y = 9

  6x - 24y = 6

Multiple Choice

Taylor Swift decided she's going to multiply the top equation by 3 and the bottom equation by 5 to create opposites. Select the new equations for Taylor Swift.

• -15x - 15y = 75

  15x + 20y = -85

• -15x - 15y = 75

  15x + 20y = 85

• -15x - 15y = -75

  15x + 20y = -85

• -15x - 15y = 75

  15x + 20y = -17

Multiple Choice

Out of the options below, what would you multiply both equations by to eliminate the y-values?

• Multiply the top equation by 9 and the bottom equation by -10

• Multiply the top equation by 9 and the bottom equation by 10

• Multiply the bottom equation by 1 only

• Multiply the top equation by 10 and the bottom equation by 9