### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem 9-146

9-146.

Solve the system of equations below for (*x*, *y*, *z*). Homework Help ✎ *x* = *y* + *z*

2*x* + 3*y* + *z* = 17

*z* + 2*y* = 7

Substitute *y* + *z* for *x* into the second equaton.

2*y* + 2*z* + 3*y* + *z* = 17

3*z* + 5*y* = 17

Multiply the third equation by −3 then add it to the earlier equation.

3*z* + 5*y* = 17

−3*z* − 6*y* = −21

−*y* = −4

Substitute 4 for *y*.

*z* + 8 = 7

Substitute 4 and −1 for *y* and *z*.

*x* = 4 − 1

*y* = 4

*z* = −1

*x* = 3

(3, 4, −1)