Question

Use the matrix tool to solve the system of equations. Choose the correct ordered pair. 4x-7y=-12 and -2+6y=11 plz help!!​

Answer 1

Answer:

Option C.

Step-by-step explanation:

Note: x is missing in the second equation.

The given equations are

$4x-7y=-12$

$-2x+6y=11$

It can we written as

$\left[\left.\begin{matrix}4 & -7\\ -2 & 6\end{matrix}\right|\begin{matrix}-12\\ 11\end{matrix}\right]$

Divide row 1 be 4.

$\left[\left.\begin{matrix}1 & -\dfrac{7}{4}\\ -2 & 6\end{matrix}\right|\begin{matrix}-3\\ 11\end{matrix}\right]$

Applying $R_2\to R_2+2R_1$, we get

$\left[\left.\begin{matrix}1 & -\dfrac{7}{4}\\ 0 & \dfrac{5}{2}\end{matrix}\right|\begin{matrix}-3\\ 5\end{matrix}\right]$

Applying $R_2\to \dfrac{2}{5}R_2$, we get

$\left[\left.\begin{matrix}1 & -\dfrac{7}{4}\\ 0 & 1\end{matrix}\right|\begin{matrix}-3\\ 2\end{matrix}\right]$

Applying $R_1\to R_1+\dfrac{7}{4}R_2$, we get

$\left[\left.\begin{matrix}1 & 0\\ 0 & 1\end{matrix}\right|\begin{matrix}\dfrac{1}{2}\\ 2\end{matrix}\right]$

Since $x=\dfrac{1}{2}\text{ and }y=2$, therefore required ordered pair is $(\dfrac{1}{2},2)$.

Hence, option C is correct.