Digits, Grade 8, Volume 2, Homework Helper

### 15-7: Solving Simultaneous Linear Equations Using Subtraction

#### Key Concept

Just as you can use addition to solve systems of linear equations, you can also use subtraction.

In the subtraction method, you solve the system by subtracting the equations to eliminate one of the variables.

Solve the system by subtraction.

table with 2 rows and 1 column , row1 column 1 , 2 x plus 1 y equals 10 , row2 column 1 , x plus 1 y equals 7 , end table

Step 1 Solve for the first variable.

table with 2 rows and 1 column , row1 column 1 , 2 x plus 1 y equals 10 , row2 column 1 , x plus 1 y equals 7 , end table

Since the coefficients of the y-terms are the same, subtract the equations to eliminate y.

table with 3 rows and 2 columns , row1 column 1 , cap writetheoriginalequations . . , column 2 2 x plus y equals 10 , row2 column 1 , cap subtracttheequations . . , column 2 table with 2 rows and 1 column , row1 column 1 , x plus y equals 7 , row2 column 1 , x plus 0 equals 3 bar , end table , row3 column 1 , cap simplify , . , column 2 x equals 3 , end table

Step 2 Solve for the second variable.

Since x = 3, substitute 3 for x in either equation and solve for y.

table with 3 rows and 3 columns , row1 column 1 , cap write , , either , , equation , . , column 2 x plus y , column 3 equals 7 , row2 column 1 , cap substitute . 3 for bold x . , column 2 3 plus y , column 3 equals 7 , row3 column 1 , solve , for bold y . , column 2 y , column 3 equals 4 , end table

Step 3 Write the solution.

Since x = 3 and y = 4, the solution is (3, 4).

Step 4 Check your solution.

Substitute the solution (3, 4) into each equation.

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