Determine whether the ordered triple is a solution of the system of equations. $$\left\{ \begin{aligned}
4 x + y - z & = 0 \
- 8 x - 6 y + z & = - \frac { 7 } { 4 } \
3 x - y & = - \frac { 9 } { 4 }
\end{aligned} \right.$$ $$\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$$

Question

Determine whether the ordered triple is a solution of the system of equations.  $$\left\{ \begin{aligned}
4 x + y - z & = 0 \
- 8 x - 6 y + z & = - \frac { 7 } { 4 } \
3 x - y & = - \frac { 9 } { 4 }
\end{aligned} \right.$$   $$\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$$

Quizplus · Accepted Answer

Substituting $x = \frac{-1}{2}$, $y = \frac{3}{4}$, and $z = \frac{-5}{4}$ into each equation of the system verifies that each equation is satisfied, making the ordered triple a solution.

Determine Whether the Ordered Triple Is a Solution of the System