7C: Solving Systems with Elimination

I understand that I am expected to have scratch paper and a writing utensil to help me truly practice some of these problems. You have 15 minutes to get those supplies before the timer on this question runs out, go go go!

• I have paper and a writing utensil

• Nah (incorrect answer, go get paper and a writing utensil)

Answer explanation

Seriously, get paper and a writing utensil! You only hurt yourself as a learner if you don't.

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

• solution of a system
• elimination method
• system of equations
• table

Tags

CCSS.HSA.REI.C.5

CCSS.HSA.REI.C.6

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.

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.

Will the solution (-3, -7) make the following system of equations a true statement?

y = 4x + 5

y = x – 4

• YES

• NO

Answer explanation

What is the first step in solving a system of equations by elimination?

• Rewrite the equations so the variables are all on the same side and line up the like terms.

• Get both equations in slope-intercept form.

• Get both equations equal to zero.

• Put the x terms first.

Answer explanation

We need all of the variables on the same side so that we can eventually add the left side of both equations together and add the right side of both equations together.

If the variables aren't on the same side of the equal-sign, then we can't combine like terms.

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.

Solve the following using elimination.

x-y=11

2x+y=19

• (10,-1)

• (-1,10)

• (-1,-10)

• (-10,-1)

Answer explanation

Solve using Elimination:

5x + y = 9

10x − 7y = −18

• (4, -11)

• (1, 4)

• (-1, 14)

• (-4, 29)

Answer explanation