Lesson Vocabulary

• substitution method

Problem 1 Using Substitution

What is the solution of the system? Use substitution.

y = 3x

x + y = − 32 x plus y equals negative 32

• Step 1 Because y = 3x, you can substitute 3x for y in x + y = − 32 . x plus y equals negative 32 .

  x + y = − 32 Write the second equation. x + 3 x = − 32 Substitute  3 x  for  y . 4 x = − 32 Simplify. x = − 8 Divide each side by  4 . table with 4 rows and 2 columns , row1 column 1 , x plus y equals negative 32 , column 2 cap write the second equation. , row2 column 1 , x plus 3 x equals negative 32 , column 2 cap substitute . 3 x , for , y . , row3 column 1 , 4 x equals negative 32 , column 2 cap simplify. , row4 column 1 , x equals negative 8 , column 2 cap divide each side by . 4 . , end table

• Step 2 Substitute − 8 negative 8  for x in either equation and solve for y.

  y = 3 x Write either equation. y = 3 ( − 8 ) = − 24 Substitute  − 8  for  x  and solve. table with 2 rows and 3 columns , row1 column 1 , y , column 2 equals 3 x , column 3 cap write either equation. , row2 column 1 , y , column 2 equals 3 open negative 8 close equals negative 24 , column 3 cap substitute . minus 8 , for , x . and solve. , end table

• The solution is ( − 8 , − 24 ) . open negative 8 comma negative 24 close .  Check by substituting ( − 8 , − 24 ) open negative 8 comma negative 24 close  into each equation.

Check

y = 3 x x + y = − 32 − 24 = ? 3 ( − 8 ) − 8 + ( − 24 ) = ? − 32 − 24 = − 24 ✓ − 32 = − 32 ✓ table with 3 rows and 4 columns , row1 column 1 , y , column 2 equals 3 x , column 3 x plus y , column 4 equals negative 32 , row2 column 1 , negative 24 , column 2 modified equals with question mark above , 3 . open , negative 8 , close , column 3 negative 8 plus . open , negative 24 , close , column 4 modified equals with question mark above , minus 32 , row3 column 1 , negative 24 , column 2 equals negative 24 check mark , column 3 negative 32 , column 4 equals negative 32 check mark , end table

✓ Got It?

1. What is the solution of the system? Use substitution. Check your answer.

   y = 2 x + 7 y = x − 1 table with 2 rows and 1 column , row1 column 1 , y equals 2 x plus 7 , row2 column 1 , y equals x minus 1 , end table