Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. ) $$\left[ \begin{array} { c c c c }
1 & 7 & \vdots & 0 \
0 & 1 & \vdots & - 1
\end{array} \right]$$
A) $$\left\{ \begin{array} { r }
x + 7 y = 0 \
y = 0
\end{array} \right.$$ (7,0)
B) $$\left\{ \begin{aligned}
x + 7 y & = 0 \
x & = - 1
\end{aligned} \right.$$ (-1,7)
C) $$\left\{ \begin{aligned}
x + 7 y & = 0 \
y & = - 1
\end{aligned} \right.$$ (7,-1)
D) $$\left\{ \begin{array} { r }
x + 7 y = 0 \
y = 1
\end{array} \right.$$ (7,1)
E) $$\left\{ \begin{aligned}
x + 7 y & = 0 \
y & = - 1
\end{aligned} \right.$$ (7,1)

Question

Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. )​ $$\left[ \begin{array} { c c c c } 
1 & 7 & \vdots & 0 \
0 & 1 & \vdots & - 1
\end{array} \right]$$ ​
A)​ $$\left\{ \begin{array} { r } 
x + 7 y = 0 \
y = 0
\end{array} \right.$$ ​​(7,0)
B)​ $$\left\{ \begin{aligned}
x + 7 y & = 0 \
x & = - 1
\end{aligned} \right.$$ ​​(-1,7)
C)​ $$\left\{ \begin{aligned}
x + 7 y & = 0 \
y & = - 1
\end{aligned} \right.$$ ​​(7,-1)
D)​ $$\left\{ \begin{array} { r } 
x + 7 y = 0 \
y = 1
\end{array} \right.$$ ​​(7,1)
E)​ $$\left\{ \begin{aligned}
x + 7 y & = 0 \
y & = - 1
\end{aligned} \right.$$ ​​​(7,1)

Quizplus · Accepted Answer

The augmented matrix directly translates to the system of equations: $x + 7y = 0$ and $y = -1$. Solving for $x$ using back substitution from $y = -1$ gives $x = 7$, hence the solution is $(7, -1)$.

Find the System of Linear Equations Represented by the Augmented [17⋮001⋮−1]\left[ \begin{array} { c c c c } 1 & 7 & \vdots & 0 \\0 & 1 & \vdots & - 1\end{array} \right]​10​71​⋮⋮​0−1​​

Find the System of Linear Equations Represented by the Augmented $\left[ \begin{array} { c c c c } 1 & 7 & \vdots & 0 \\0 & 1 & \vdots & - 1\end{array} \right]$