Answer: B. (-1, -5)
Explanation:
Given equations
2x + y = -7
x - y = 4
Concept
![A^(-1)=(1)/(ad-bc)\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/w9p02cjn80eymv3mcxw3rsmotdn3o7y0ft.png)

Convert into matrix
![\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/vqgyc6l9608btw4f11fwve6n5k7ger4s6g.png)
Calculate the inverse of the matrix
![A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/94ntpt7cwixpzd8t18g4f3u0wj5duiv7od.png)
![A^(-1)=(1)/(ad-bc)\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/w9p02cjn80eymv3mcxw3rsmotdn3o7y0ft.png)
![A^(-1)=-(1)/(3) \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/b1u4deqhxkqr63lj1bfkdbdg3rh3yfatm9.png)
Solve by multiplying the inverse of the matrix

![-(1)/(3) \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-(1)/(3) \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/jmib5x5qger7vp3ktfdbwjey8t4fms7e7y.png)
![1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-(1)/(3)\left[\begin{array}{ccc}3\\15\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/txs5ztnwrh371s2nbe2yu1u4hmxxh8ry22.png)
Simplify by multiplication
![\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right]](https://img.qammunity.org/2023/formulas/mathematics/college/p3a8ierzyq6g5hz510nqnjti5c70r6ubpd.png)
Therefore, the answer is

Hope this helps!! :)
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