IXL - Solve a system of equations using elimination (Algebra 2 practice)

Solve using elimination.

3x + 8y = ^–11

^–7x − 8y = ^–17

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question

Solve using elimination.

^–9x − 8y = 19

10x + 8y = ^–14

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key idea

To solve using elimination, follow these four steps:

Step 1: Make sure the equations have opposite x terms or opposite y terms.

Step 2: Add to eliminate one variable and solve for the other.

Step 3: Plug the result of Step 2 into one of the original equations and solve.

Step 4: State the solution.

solution

Use elimination to solve the system of equations:

^–9x − 8y = 19

10x + 8y = ^–14

Step 1: Make sure the equations have opposite x terms or opposite y terms.

The y terms (^–8y and 8y) are already opposites.

Step 2: Add to eliminate one variable and solve for the other.

Add to eliminate the y terms, and then solve for x.

Add to eliminate the y terms
	^–9x	−	8y	=	19
+ (	10x	+	8y	=	^–14	)


	x	+	0y	=	5	Add to eliminate the y terms

Simplify
			x	=	5	Simplify

Step 3: Plug the result of Step 2 into one of the original equations and solve.

Take the result of Step 2, x = 5, and plug it into one of the original equations, such as ^–9x + ^–8y = 19. Then find the value of y.

^–9x − 8y

Plug in x = 5

^–9(5) − 8y

Plug in x = 5

Multiply

^–45 − 8y

Multiply

Add 45 to both sides

^–8y

Add 45 to both sides

Divide both sides by ^–8

^–8

Divide both sides by ^–8

Step 4: State the solution.

Since x = 5 and y = ^–8, the solution is (5, ^–8).

Looking for more? Try these:

Lesson: Systems of equations

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Not feeling ready yet? These can help:

B.1Solve linear equations

B.9Simplify variable expressions involving like terms and the distributive property

Lesson: Systems of equations

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