Problem 3 Solving by Elimination

What is the solution of the system of equations?

{ 4 x + 2 y = 9 − 4 x + 3 y = 16 left brace . table with 2 rows and 1 column , row1 column 1 , 4 x plus 2 y equals 9 , row2 column 1 , negative 4 x plus 3 y equals 16 , end table

4 x + 2 y = 9   − 4 x + 3 y = 16 ▲ One equation has  4 x  and the other has − 4 x . Add to eliminate the variable  x . 5 y = 25   y = 5 Solve for  y . 4 x + 2 y = 9 Choose one of the original equations. 4 x + 2 ( 5 ) = 9 Substitute for  y . 4 x = − 1 Solve for  x . x = − 1 4   table with 3 rows and 1 column , row1 column 1 , table with 3 rows and 3 columns , row1 column 1 , 4 x plus 2 y , column 2 equals 9 , column 3 , row2 column 1 , negative 4 x plus 3 y , column 2 equals 16 , row3 column 1 , black up pointing triangle , end table , row2 column 1 , table with 2 rows and 1 column , row1 column 1 , cap one equation has . 4 x . and the other has , row2 column 1 , negative 4 x . . cap add to eliminate the variable . x . , end table , row3 column 1 , table with 6 rows and 3 columns , row1 column 1 , 5 y , column 2 equals 25 , column 3 , row2 column 1 , y , column 2 equals 5 , column 3 cap solve for . y . , row3 column 1 , 4 x plus 2 y , column 2 equals 9 , column 3 cap choose one of the original equations. , row4 column 1 , 4 x plus 2 open 5 close , column 2 equals 9 , column 3 cap substitute for . y . , row5 column 1 , 4 x , column 2 equals negative 1 , column 3 cap solve for . x . , row6 column 1 , x , column 2 equals negative , 1 fourth , column 3 , end table , end table

The solution is ( − 1 4 , 5 ) . open negative , 1 fourth . comma 5 close .

✓ Got It?

3. What is the solution of the system of equations? { − 2 x + 8 y = − 8 5 x − 8 y = 20 left brace . table with 2 rows and 1 column , row1 column 1 , negative 2 x plus 8 y equals negative 8 , row2 column 1 , 5 x minus 8 y equals 20 , end table

Problem 4 Solving an Equivalent System

What is the solution of the system of equations? 1 2 { 2 x + 7 y = 4 3 x + 5 y = − 5 table with 1 row and 2 columns , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , begin circle , 1 , end circle , row2 column 1 , begin circle , 2 , end circle , end table , column 2 left brace . table with 2 rows and 1 column , row1 column 1 , 2 x plus 7 y equals 4 , row2 column 1 , 3 x plus 5 y equals negative 5 , end table , end table