Solve the system.
-$$\left\{ \begin{aligned}
x + y + z & = 7 \
x - y + 5 z & = - 3 \
4 x + y + z & = 22
\end{aligned} \right.$$
A) $( 5,3 , - 1 )$
B) $( - 1,3,5 )$
C) $( - 1,5,3 )$
D) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the system of equations, we can use either substitution or elimination. Here, adding the first and second equations eliminates $y$, giving $2x + 6z = 4$, or $x + 3z = 2$. Adding the first and third equations gives $5x + 2z = 29$. Solving these two new equations for $x$ and $z$ gives $x = 5$ and $z = -1$. Substituting these into the first original equation gives $y = 3$. Thus, the solution is $(5, 3, -1)$.

Solve the System {x+y+z=7x−y+5z=−34x+y+z=22\left\{ \begin{aligned}x + y + z & = 7 \\x - y + 5 z & = - 3 \\4 x + y + z & = 22\end{aligned} \right.⎩⎨⎧​x+y+zx−y+5z4x+y+z​=7=−3=22​

Solve the System $\left\{ \begin{aligned}x + y + z & = 7 \\x - y + 5 z & = - 3 \\4 x + y + z & = 22\end{aligned} \right.$