Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem9-146

9-146.

Solve the system of equations below for $\left(x, y, z\right)$.

$x = y + z\\2x + 3y + z = 17\\ z + 2y = 7$

Substitute y + z for x into the second equaton.

$2y + 2z + 3y + z = 173\\z + 5y = 17$

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

$3z + 5y = 17\\−3z − 6y = −21$

$−y = −4$

Substitute 4 for y.

$z + 8 = 7$

Substitute 4 and −1 for y and z.

$x = 4 − 1$

$y = 4$

$z = −1$

$x = 3$

$\left(3, 4, −1\right)$