Home > A2C > Chapter 10 > Lesson 10.1.2 > Problem10-48

10-48.

Solve the system of equations below.

$8x − 3y − 2z = −8 \\−2x + 8y + 7z = 26\\ 4x + y − 5z = 23$

$8x − 3y − 2z = −8 →$

$4\left(−2x + 8y + 7z = 26\right) →$

$2\left(−2x + 8y + 7z = 26\right) →$

$4x + y − 5z = 23 →$

$8x − 3y − 2z = −8$

$−8x + 32y + 28z = 104$

$29y + 26z = 96 \left(a\right)$

$−4x + 16 + 14z = 52$

$4x + y − 5z = 23$

$17y + 9z = 75 \left(b\right)$

Now use (a) and (b) to find $y$ and $z$, and then find $x$.

$\left(\frac{1}{2},\,6,\,-3\right)$