Solve the system,if possible. ?? $$\left\{ \begin{array} { l }
x + y = - 9 \
y + z = - 15 \
2 x - z = 7
\end{array} \right.$$ ?
A)x = -9,y = 12,z = 5
B)x = 1,y = -10,z = -5
C)x = -1,y = 10,z = 5
D)x = -9,y = 1,z = 5
E)no solution;inconsistent system

Question

Solve the system,if possible. ?? $$\left\{ \begin{array} { l } 
x + y = - 9 \
y + z = - 15 \
2 x - z = 7
\end{array} \right.$$ ?
A)x = -9,y = 12,z = 5
B)x = 1,y = -10,z = -5
C)x = -1,y = 10,z = 5
D)x = -9,y = 1,z = 5
E)no solution;inconsistent system

Quizplus · Accepted Answer

To solve the system of equations, we can use substitution or elimination. First, solve the first equation for $x$: $x = -9 - y$. Then, substitute $x$ into the third equation: $2(-9 - y) - z = 7$, which simplifies to $-18 - 2y - z = 7$, or $2y + z = -25$. However, this approach was incorrect in simplification; let's correct the approach:1. From the first equation, $x = -9 - y$.2. From the second equation, $z = -15 - y$.3. Substitute $x$ and $z$ into the third equation: $2(-9 - y) - (-15 - y) = 7$, which simplifies to $-18 - 2y + 15 + y = 7$, leading to $-3 - y = 7$, and further simplification gives $y = -10$.4. Substitute $y = -10$ into $x = -9 - y$ to find $x = 1$.5. Substitute $y = -10$ into $z = -15 - y$ to find $z = -5$.Therefore, the solution is $x = 1$, $y = -10$, and $z = -5$, which corresponds to choice B.

Solve the System,if Possible {x+y=−9y+z=−152x−z=7\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.⎩⎨⎧​x+y=−9y+z=−152x−z=7​

Solve the System,if Possible $\left\{ \begin{array} { l } x + y = - 9 \\y + z = - 15 \\2 x - z = 7\end{array} \right.$