$\left\{ \begin{aligned}
x + 5 y + 2 z & = 33 \
5 y + 5 z & = 45 \
z & = 5
\end{aligned} \right.$
A) x=5, y=4, z=3
B) No solution
C) x=3, y=4, z=5
D) x=3, y=5, z=4

Question

$\left\{ \begin{aligned}
x + 5 y + 2 z & = 33 \
5 y + 5 z & = 45 \
z & = 5
\end{aligned} \right.$
A)  x=5, y=4, z=3 
B) No solution
C)  x=3, y=4, z=5 
D)  x=3, y=5, z=4

Quizplus · Accepted Answer

Given $z = 5$, substituting into the second equation gives $5y + 5(5) = 45$, which simplifies to $5y + 25 = 45$, leading to $5y = 20$, and thus $y = 4$. Substituting $y = 4$ and $z = 5$ into the first equation gives $x + 5(4) + 2(5) = 33$, which simplifies to $x + 20 + 10 = 33$, leading to $x = 3$. Therefore, $x = 3$, $y = 4$, and $z = 5$.

{x+5y+2z=335y+5z=45z=5\left\{ \begin{aligned}x + 5 y + 2 z & = 33 \\5 y + 5 z & = 45 \\z & = 5\end{aligned} \right.⎩⎨⎧​x+5y+2z5y+5zz​=33=45=5​

$\left\{ \begin{aligned}x + 5 y + 2 z & = 33 \\5 y + 5 z & = 45 \\z & = 5\end{aligned} \right.$