IXL | Solve a system of equations using any method

Solve.

^–6x + 8y = ^–10

^–2x + y = 5

(, )

ref_doc_title.

Learn with an example

question

Solve.

^–3x − 4y = 9

^–4x − 4y = 16

(, )

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 any method to solve the system of equations, such as elimination.

^–3x − 4y = 9

^–4x − 4y = 16

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

Currently, neither the x terms (^–3x and ^–4x) nor the y terms (^–4y and ^–4y) 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 − 4y = 9)

→

3x + 4y = ^–9

^–4x + ^–4y = 16

→

^–4x − 4y = 16

Now the y terms (4y and ^–4y) are 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
	3x	+	4y	=	^–9
+ (	^–4x	−	4y	=	16	)


	^–x	+	0y	=	7	Add to eliminate the y terms

Simplify
			^–x	=	7	Simplify

Multiply both sides by ^–1
			x	=	^–7	Multiply both sides by ^–1

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

Take the result of Step 2, x = ^–7, and plug it into one of the original equations, such as ^–3x + ^–4y = 9. Then find the value of y.

^–3x − 4y

Plug in x = ^–7

^–3(^–7) − 4y

Plug in x = ^–7

Multiply

21 − 4y

Multiply

Subtract 21 from both sides

^–4y

^–12

Subtract 21 from both sides

Divide both sides by ^–4

Step 4: State the solution.

Since x = ^–7 and y = 3, the solution is (^–7, 3).

Looking for more? Try these:

Lesson: Systems of equations

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.10Solve a system of equations using elimination

GG.8Solve a system of equations using substitution

Lesson: Systems of equations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!