CPM Homework Help : A2C Problem 9-146

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

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

Step 1:

Substitute y + z for x into the second equaton.

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

Step 2:

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

$3z + 5y = 17\\−3z − 6y = −21$

$−y = −4$

Step 3:

Substitute 4 for y.

$z + 8 = 7$

Step 4:

Substitute 4 and −1 for y and z.

$x = 4 − 1$

Answer 1:

$y = 4$

Answer 2:

$z = −1$

Answer 3:

$x = 3$

Answer 4:

$\left(3, 4, −1\right)$