Substitution and Elimination Methods for Systems of Equations Quick Check

Consider the given system. Which variable is best eliminated first?

Answer explanation

The variable x is best eliminated first because its coefficients are already additive inverses of each other.

Recall that 4x−4x=0.

Which two equations would help you eliminate the variable y?

Answer explanation

To eliminate the variable y, both coefficients from the two equations should be additive inverses of each other.

The LCM of 4 and 9 is 36. Thus, you multiply the first equation by 9:

9(5x+4y=−30)

45x+36y=−270

Then, you multiply the second equation by 4:

4(3x−9y=−18)

12x−36y=−72

The new equations can now be added and the y variables can now be eliminated.

Which of the following is a good start when using the elimination method to solve this system?

• multiplying the second equation by 1

• multiplying the first equation by -2

• multiplying the second equation by -1

• multiplying the first equation by 2

Answer explanation

The idea behind the elimination method is to cancel one of the variables. In order for this to be possible, the coefficients of this variable need to have the same absolute value and opposite signs.

In this example, if we multiply the second equation by −1, we would then be able to add the variable x in the first equation with −x in the second one which will result to cancellation of the said variable.

Therefore, the correct answer is multiplying the second equation by −1.

Solve the system using any method:

3x + 2y = 16

7x + y = 19

Answer is (​ (a)   ,​ (b)   )

• 2

• 5

• 1

• 3

• 4

• 7

• 16

• 19

• 0

• No solution

Solve the system for y:

x - y = 10

2x + 2y = 8

Mathematical Equivalence

OFF

Solve the system of equations.

8x-6y=16

4x+2y=22​ (a)  

What is the x value of the solution?

• 4.1

• -10/3

• 2.8

• -2

Solve the system.

• A

• B

• C

• D

• 2

• -7

• 3

• -10

• -5

• -8

• -2

• -6

• 3

• 2

• 6

• 1

• 0

• -3

• 4

• 5

Solve the system for y:

2x + y = 15

-2x + 3y = 25

Mathematical Equivalence

OFF