Determine whether the ordered triple is a solution of the system of equations.? $$\left\{ \begin{aligned}
4 x + y - z & = 0 \
- 8 x - 6 y + z & = - \frac { 7 } { 4 } \
3 x - y & = - \frac { 9 } { 4 }
\end{aligned} \right.$$ ? $$\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$$ ? ?
A)Yes
B)No

Question

Quizplus · Accepted Answer

To verify if the ordered triple $\left( \frac { - 1 } { 2 } , \frac { 3 } { 4 } , \frac { - 5 } { 4 } \right)$ is a solution, substitute $x = \frac { - 1 } { 2 }$, $y = \frac { 3 } { 4 }$, and $z = \frac { - 5 } { 4 }$ into each equation. For the first equation, $4\left(\frac{-1}{2}\right) + \frac{3}{4} - \frac{-5}{4} = -2 + \frac{3}{4} + \frac{5}{4} = 0$. For the second equation, $-8\left(\frac{-1}{2}\right) - 6\left(\frac{3}{4}\right) + \frac{-5}{4} = 4 - \frac{9}{2} - \frac{5}{4} = 4 - 4.5 - 1.25 = -\frac{7}{4}$. For the third equation, $3\left(\frac{-1}{2}\right) - \frac{3}{4} = -\frac{3}{2} - \frac{3}{4} = -\frac{9}{4}$. Since all equations are satisfied, the ordered triple is indeed a solution.

Determine Whether the Ordered Triple Is a Solution of the System