QUICK CHECK & LESSON ECHOES

Which of the following methods are used to solve systems of linear equations algebraically?

• The substitution method and the division method

• The subtraction method and the elimination method

• The elimination method and the division method

• The substitution method and the elimination method

Answer explanation

Two of the most common techniques used for solving systems of linear equations are the elimination method and the substitution method. Both are equally used in general.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Consider the given system.

Answer explanation

The first equation, 5x+y=9, should be multiplied by 7.

7(5x+y=9)

35x+7y=63

The new system will be:

35x+7y=63

10x−7y=−18

Adding the left and right sides of the equation would cancel the y variable because 7y−7y=0.

Tags

CCSS.HSA.REI.C.9

Consider the given system.

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Consider the following system of linear equations.

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the given system of linear equations.

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following system of linear equations:

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following system of linear equations:

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the following system of linear equations:

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Solve the given system of linear equations:

Answer explanation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6