CPM Homework Help : CCA2 Problem 8-144

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

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

Step 1:

Substitute $y + z$ for $x$ into the second equation.

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

Step 2:

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

$3z + 5y = 17$
$−3z − 6y = −21$
$-y = -4$
$y = 4$

Step 3:

Substitute 4 for y in the third equation to solve for $z$ .

$z + 8 = 7$
$z = -1$

Step 4:

Substitute $4$ for y and $−1$ for $z$ in the first equation to solve for $x$ .

$x = 4 − 1$
$x = 3$

Step 5:

Check your values for $x, y,$ and $z$ in the second equation.

Answer:

$(3, 4, -1)$