Solve the system of linear equations $\left\{ \begin{array} { l }
4 x + 4 y = 3 \
8 x - 20 y = - 9
\end{array} \right.$ using an inverse matrix.
A) $\left[ \begin{array} { l }
x \
y
\end{array} \right] = \left[ \begin{array} { l }
\frac { 3 } { 14 } \
\frac { 15 } { 28 }
\end{array} \right]$
B) $\left[ \begin{array} { l }
x \
y
\end{array} \right] = \left[ \begin{array} { l }
\frac { 9 } { 28 } \
\frac { 12 } { 7 }
\end{array} \right]$
C) $\left[ \begin{array} { l }
x \
y
\end{array} \right] = \left[ \begin{array} { c }
\frac { 9 } { 28 } \
\frac { - 3 } { 14 }
\end{array} \right]$
D) $\left[ \begin{array} { l }
x \
y
\end{array} \right] = \left[ \begin{array} { c }
\frac { 9 } { 7 } \
\frac { 15 } { 28 }
\end{array} \right]$
E) $\left[ \begin{array} { l }
x \
y
\end{array} \right] = \left[ \begin{array} { c }
\frac { - 9 } { 7 } \
\frac { - 3 } { 14 }
\end{array} \right]$

Question

Solve the system of linear equations $\left\{ \begin{array} { l } 
4 x + 4 y = 3 \
8 x - 20 y = - 9
\end{array} \right.$ using an inverse matrix.
A)  $\left[ \begin{array} { l } 
x \
y
\end{array} \right] = \left[ \begin{array} { l } 
\frac { 3 } { 14 } \
\frac { 15 } { 28 }
\end{array} \right]$
B)  $\left[ \begin{array} { l } 
x \
y
\end{array} \right] = \left[ \begin{array} { l } 
\frac { 9 } { 28 } \
\frac { 12 } { 7 }
\end{array} \right]$
C)  $\left[ \begin{array} { l } 
x \
y
\end{array} \right] = \left[ \begin{array} { c } 
\frac { 9 } { 28 } \
\frac { - 3 } { 14 }
\end{array} \right]$
D)  $\left[ \begin{array} { l } 
x \
y
\end{array} \right] = \left[ \begin{array} { c } 
\frac { 9 } { 7 } \
\frac { 15 } { 28 }
\end{array} \right]$
E)  $\left[ \begin{array} { l } 
x \
y
\end{array} \right] = \left[ \begin{array} { c } 
\frac { - 9 } { 7 } \
\frac { - 3 } { 14 }
\end{array} \right]$

Quizplus · Accepted Answer

The correct answer is A because the inverse of the coefficient matrix is $\left[ \begin{array} { c c } \frac { 1 } { 14 } & \frac { 1 } { 7 } \\frac { 1 } { 2 } & \frac { - 1 } { 4 }\end{array} \right]$ and the solution is $\left[ \begin{array} { l } x \y\end{array} \right] = \left[ \begin{array} { c c } \frac { 1 } { 14 } & \frac { 1 } { 7 } \\frac { 1 } { 2 } & \frac { - 1 } { 4 }\end{array} \right] \left[ \begin{array} { l } 3 \- 9\end{array} \right] = \left[ \begin{array} { l } \frac { 3 } { 14 } \\frac { 15 } { 28 }\end{array} \right]$.

Solve the System of Linear Equations {4x+4y=38x−20y=−9\left\{ \begin{array} { l } 4 x + 4 y = 3 \\8 x - 20 y = - 9\end{array} \right.{4x+4y=38x−20y=−9​

Solve the System of Linear Equations $\left\{ \begin{array} { l } 4 x + 4 y = 3 \\8 x - 20 y = - 9\end{array} \right.$