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

Solve using elimination.

^–x + 5y = ^–14

3x − 5y = 2

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question

Solve using elimination.

^–x + 4y = ^–16

x + 2y = ^–20

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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:

^–x + 4y = ^–16

x + 2y = ^–20

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

The x terms (^–x and x) are already opposites.

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

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

Add to eliminate the x terms
	^–x	+	4y	=	^–16
+ (	x	+	2y	=	^–20	)


	0x	+	6y	=	^–36	Add to eliminate the x terms

Simplify
			6y	=	^–36	Simplify

Divide both sides by 6
			y	=	^–6	Divide both sides by 6

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

Take the result of Step 2, y = ^–6, and plug it into one of the original equations, such as ^–x + 4y = ^–16. Then find the value of x.

^–x + 4y

^–16

Plug in y = ^–6

^–x + 4(^–6)

^–16

Plug in y = ^–6

Multiply

^–x − 24

^–16

Multiply

Add 24 to both sides

^–x

Add 24 to both sides

Multiply both sides by ^–1

^–8

Multiply both sides by ^–1

Step 4: State the solution.

Since x = ^–8 and y = ^–6, the solution is (^–8, ^–6).

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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