Digits, Grade 8, Volume 1, Homework Helper

### 8-4: Solving Simultaneous Linear Equations Using Substitution

#### Key Concept

You can solve simultaneous linear equations using an algebraic method called the substitution method. Solve one of the equations for one of the variables. Then substitute the expression for the variable into the other equation and solve for the second variable.

Solve the system by substitution.

y = 3x

2x + y = 15

• Step 1 Solve for the first variable.

Since y = 3x, you can substitute 3x for y in 2x + y = 15.

table with 4 rows and 3 columns , row1 column 1 , cap write , , the , , second , . equehtion . . , column 2 2 x plus y , column 3 equals 15 , row2 column 1 , cap substitute . 3 . bold italic x . , for , . bold italic y . , column 2 2 x plus 3 x , column 3 equals 15 , row3 column 1 , cap simplify , . , column 2 5 x , column 3 equals 15 , row4 column 1 , cap divide , , eehch , , side , by 5 . . , column 2 x , column 3 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 , . equehtion . . , column 2 y , column 3 equals 3 x , row2 column 1 , cap substitute . 3 , for , . bold italic x . , column 2 y , column 3 equals 3 open 3 close , row3 column 1 , cap simplify , . , column 2 y , column 3 equals 9 , end table

• Step 3 Write the solution.

Since x = 3, and y = 9, the solution is (3, 9).

• Step 4 Check your solution.

Substitute the solution (3, 9) into each equation.

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