IXL - Solve a system of equations by adding or subtracting (Algebra 1 practice)

Solve using elimination.

x − 2y = 1

5x + 2y = ^–7

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question

Solve using elimination.

^–x − 10y = ^–20

2x + 10y = 10

(, )

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 − 10y = ^–20

2x + 10y = 10

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

The y terms (^–10y and 10y) 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
	^–x	−	10y	=	^–20
+ (	2x	+	10y	=	10	)


	x	+	0y	=	^–10	Add to eliminate the y terms

Simplify
			x	=	^–10	Simplify

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

Take the result of Step 2, x = ^–10, and plug it into one of the original equations, such as ^–x + ^–10y = ^–20. Then find the value of y.

^–x − 10y

^–20

Plug in x = ^–10

10 − 10y

^–20

Plug in x = ^–10

Subtract 10 from both sides

^–10y

^–30

Subtract 10 from both sides

Divide both sides by ^–10

Step 4: State the solution.

Since x = ^–10 and y = 3, the solution is (^–10, 3).

Looking for more? Try these:

Lesson: Systems of equations

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C.10Solve linear equations with variables on one side

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

Lesson: Systems of equations

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