Solve the system of equations.
-$$\begin{aligned}
x - y + 5 z & = - 3 \
1 x + z & = 0 \
x + 3 y + z & = 9
\end{aligned}$$
A) $\{ ( 0,3,0 ) \}$
B) $\{ ( 0,0,3 ) \}$
C) $\{ ( 0,3 , - 3 ) \}$
D) $\{ ( 3,0,0 ) \}$

Question

Quizplus · Accepted Answer

To solve the system of equations, we can use substitution or elimination. From the second equation, $x + z = 0$, we can express $x$ in terms of $z$: $x = -z$. Substituting $x = -z$ into the first and third equations:1. $(-z) - y + 5z = -3$ simplifies to $4z - y = -3$.2. $(-z) + 3y + z = 9$ simplifies to $3y = 9$, which means $y = 3$.Substituting $y = 3$ into the simplified first equation, we get $4z - 3 = -3$, which simplifies to $4z = 0$, so $z = 0$. Then, substituting $z = 0$ back into $x = -z$, we get $x = 0$.Therefore, the solution is $(x, y, z) = (0, 3, 0)$.

Solve the System of Equations x−y+5z=−31x+z=0x+3y+z=9\begin{aligned}x - y + 5 z & = - 3 \\1 x + z & = 0 \\x + 3 y + z & = 9\end{aligned}x−y+5z1x+zx+3y+z​=−3=0=9​

Solve the System of Equations $\begin{aligned}x - y + 5 z & = - 3 \\1 x + z & = 0 \\x + 3 y + z & = 9\end{aligned}$