Determine whether $\left( 3 , - \frac { 1 } { 2 } , - 1 \right)$ is a solution of the system $\left\{ \begin{array} { l }
x - 2 y - z = 5 \
3 x - 4 y + z = 10 \
5 x - 2 y + z = 15
\end{array} \right.$ .
A) not a solution
B) solution

Question

Determine whether $\left( 3 , - \frac { 1 } { 2 } , - 1 \right)$ is a solution of the system $\left\{ \begin{array} { l } 
x - 2 y - z = 5 \
3 x - 4 y + z = 10 \
5 x - 2 y + z = 15
\end{array} \right.$ .
A) not a solution
B) solution

Quizplus · Accepted Answer

Substitute $x = 3$, $y = -\frac{1}{2}$, $z = -1$ into each equation:  1. $3 - 2(-\frac{1}{2}) - (-1) = 3 + 1 + 1 = 5$ (True)  2. $3(3) - 4(-\frac{1}{2}) + (-1) = 9 + 2 - 1 = 10$ (True)  3. $5(3) - 2(-\frac{1}{2}) + (-1) = 15 + 1 - 1 = 15$ (True)  All equations are satisfied, so it is a solution.

Determine Whether (3,−12,−1)\left( 3 , - \frac { 1 } { 2 } , - 1 \right)(3,−21​,−1)

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