IXL - Solve a system of equations using elimination (Algebra 1 practice)

Solve using elimination.

6x − y = ^–2

6x − 4y = 10

(, )

ref_doc_title.

Learn with an example

question

Solve using elimination.

4x + 5y = 14

^–7x − 5y = 13

(, )

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:

4x + 5y = 14

^–7x − 5y = 13

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

The y terms (5y and ^–5y) 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
	4x	+	5y	=	14
+ (	^–7x	−	5y	=	13	)


	^–3x	+	0y	=	27	Add to eliminate the y terms

Simplify
			^–3x	=	27	Simplify

Divide both sides by ^–3
			x	=	^–9	Divide both sides by ^–3

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

Take the result of Step 2, x = ^–9, and plug it into one of the original equations, such as 4x + 5y = 14. Then find the value of y.

4x + 5y

Plug in x = ^–9

4(^–9) + 5y

Plug in x = ^–9

Multiply

^–36 + 5y

Multiply

Add 36 to both sides

Divide both sides by 5

Step 4: State the solution.

Since x = ^–9 and y = 10, the solution is (^–9, 10).

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	06

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:

C.10Solve linear equations with variables on one side

O.1Is (x, y) a solution to the system of equations?

Lesson: Systems of equations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!