IXL | Solve a system of equations using elimination

Solve using elimination.

x − y = 3

x + y = 11

(, )

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Learn with an example

question

Solve using elimination.

^–3x − 6y = ^–9

^–3x − 2y = 11

(, )

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:

^–3x − 6y = ^–9

^–3x − 2y = 11

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

Currently, neither the x terms (^–3x and ^–3x) nor the y terms (^–6y and ^–2y) are opposites. Use multiplication to rewrite the equations with either opposite x terms or opposite y terms. One good approach is to multiply the first equation by ^–1.

^–(^–3x − 6y = ^–9)

→

3x + 6y = 9

^–3x + ^–2y = 11

→

^–3x − 2y = 11

Now the x terms (3x and ^–3x) are 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
	3x	+	6y	=	9
+ (	^–3x	−	2y	=	11	)


	0x	+	4y	=	20	Add to eliminate the x terms

Simplify
			4y	=	20	Simplify

Divide both sides by 4
			y	=	5	Divide both sides by 4

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

Take the result of Step 2, y = 5, and plug it into one of the original equations, such as ^–3x + ^–6y = ^–9. Then find the value of x.

^–3x − 6y

^–9

Plug in y = 5

^–3x − 6(5)

^–9

Plug in y = 5

Multiply

^–3x − 30

^–9

Multiply

Add 30 to both sides

^–3x

Add 30 to both sides

Divide both sides by ^–3

^–7

Divide both sides by ^–3

Step 4: State the solution.

Since x = ^–7 and y = 5, the solution is (^–7, 5).

Looking for more? Try these:

Lesson: Systems of equations

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Lesson: Systems of equations

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