Lesson Vocabulary

• elimination method

Problem 1 Solving a System by Adding Equations

What is the solution of the system? Use elimination.

2 x + 5 y = 17 6 x − 5 y = − 9 table with 2 rows and 1 column , row1 column 1 , 2 bold italic x plus 5 bold italic y equals 17 , row2 column 1 , 6 bold italic x minus 5 bold italic y equals negative 9 , end table

• Step 1 Eliminate one variable. Since the sum of the coefficients of y is 0, add the equations to eliminate y.

  2 x + 5 y = 17 6 x − 5 y = − 9 _   8 x + 0 = 8 x = 1 Add the two equations . Solve for  x . table with 2 rows and 2 columns , row1 column 1 , modified table with 2 rows and 2 columns , row1 column 1 , 2 x plus 5 y , column 2 equals 17 , row2 column 1 , 6 x minus 5 y , column 2 equals negative 9 , end table with under bar below , column 2 , row2 column 1 , table with 2 rows and 2 columns , row1 column 1 , 8 x plus 0 , column 2 equals 8 , row2 column 1 , x , column 2 equals 1 , end table , column 2 table with 2 rows and 1 column , row1 column 1 , cap addthetwoequations . . , row2 column 1 , cap solvefor . x . , end table , end table

• Step 2 Substitute 1 for x to solve for the eliminated variable.

  2 x + 5 y = 17 You can use the first equation . 2 ( 1 ) + 5 y = 17 Substitute  1  for  x . 2 + 5 y = 17 Simplify . y = 3 Solve for y . table with 4 rows and 3 columns , row1 column 1 , 2 x plus 5 y , column 2 equals 17 , column 3 cap youcanusethefirstequation . . , row2 column 1 , 2 , open 1 close , plus 5 y , column 2 equals 17 , column 3 cap substitute . 1 , for , x . , row3 column 1 , 2 plus 5 y , column 2 equals 17 , column 3 cap simplify , . , row4 column 1 , y , column 2 equals 3 , column 3 cap solvefory . . , end table

Since x = 1 and y = 3, the solution is (1, 3).