Systems of Equations Elimination

What can be done to one of the equations below in order to be able to eliminate a variable?

4x + 3y = 22

2x -y = -14

• Multiply the top equation by 4

• Multiply the top equation by 3

• Multiply the bottom equation by 4

• Multiply the bottom equation by 3

What can be done to one of the equations below in order to be able to eliminate a variable?

6x + 4y = 14

-9x - 8y = -25

• Multiply the top equation by 6

• Multiply the top equation by 2

• Multiply the bottom equation by 6

• Multiply the bottom equation by 2

What can be done to one of the equations below in order to be able to eliminate a variable? Select all options that would work.

-8x + 8 y = 16

4x -2y = 6

• Multiply the top equation by 4

• Multiply the top equation by 2

• Multiply the bottom equation by 4

• Multiply the bottom equation by 2

Which of the following is NOT a method to solve systems?

• Elimination

• Distribution

• Substitution

• Graphing

Answer explanation

You may at times need to use distribution to help you solve a system of equations, but it is not the overall method.

Distribution is a property that helps us to simplify equations and expressions.

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.

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4

• YES
• NO

Which variable has opposite coefficients?

• X

• Y

a solution to a system that results in an unlimited amount of x values and an unlimited amount of y values that will satisfy both equations

• No Solution
• One Solution
• Infinite Solutions
• Beyond Solutions