Lesson Vocabulary

• equivalent systems

Problem 1 Solving by Substitution

What is the solution of the system of equations? { 3 x + 4 y = 12 2 x + y = 10 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus 4 y equals 12 , row2 column 1 , 2 x plus y equals 10 , end table

• Step 1 Solve one equation for one of the variables.

  2 x + y = 10 y = − 2 x + 10 table with 2 rows and 2 columns , row1 column 1 , 2 x plus y , column 2 equals 10 , row2 column 1 , y , column 2 equals negative 2 x plus 10 , end table

• Step 2 Substitute the expression for y in the other equation. Solve for x.

  3 x + 4 y = 12 3 x + 4 ( − 2 x + 10 ) = 12 3 x − 8 x + 40 = 12 x = 5.6 table with 4 rows and 2 columns , row1 column 1 , 3 x plus 4 y , column 2 equals 12 , row2 column 1 , 3 x plus 4 open negative 2 x plus 10 close , column 2 equals 12 , row3 column 1 , 3 x minus 8 x plus 40 , column 2 equals 12 , row4 column 1 , x , column 2 equals 5.6 , end table

• Step 3 Substitute the value for x into one of the original equations. Solve for y.

  2 x + y = 10 2 ( 5.6 ) + y = 10 11.2 + y = 10 y = − 1.2 table with 4 rows and 2 columns , row1 column 1 , 2 x plus y , column 2 equals 10 , row2 column 1 , 2 open 5.6 close plus y , column 2 equals 10 , row3 column 1 , 11.2 , plus y , column 2 equals 10 , row4 column 1 , y , column 2 equals negative 1.2 , end table

The solution is ( 5 . 6 , − 1 . 2 ) . open 5 . 6 comma negative 1 . 2 close .

✓ Got It?

1. What is the solution of the system of equations? { x + 3 y = 5 − 2 x − 4 y = − 5 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 3 y equals 5 , row2 column 1 , negative 2 x minus 4 y equals negative 5 , end table