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

Option C.

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 & -(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 & -(7)/(4)\\ 0 & (5)/(2)\end{matrix}\right|\begin{matrix}-3\\ 5\end{matrix}\right]`

Applying
`R_2\to (2)/(5)R_2`, we get

`\left[\left.\begin{matrix}1 & -(7)/(4)\\ 0 & 1\end{matrix}\right|\begin{matrix}-3\\ 2\end{matrix}\right]`

Applying
`R_1\to R_1+(7)/(4)R_2`, we get

`\left[\left.\begin{matrix}1 & 0\\ 0 & 1\end{matrix}\right|\begin{matrix}(1)/(2)\\ 2\end{matrix}\right]`

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

Hence, option C is correct.