Question

What is the solution of the matrix equation

Answer 1

`\left[\begin{array}{ccc}1&1\\2&3\end{array}\right]\ \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}8\\36\end{array}\right]\\ \left[\begin{array}{ccc}1x+1y\\2x+3y\end{array}\right] =\left[\begin{array}{ccc}8\\36\end{array}\right]\to\left\{\begin{array}{ccc}x+y=8&|\cdot(-2)\\2x+3y=36\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y=-16\\2x+3y=36\end{array}\right}\ |\text{add both sides of equations}\\.\ \ \ \ \ \ \ \ \ \ y=20`

`\\\text{substitute the value of y to the first equation}\\\\x+20=8\ \ \ |-20\\\\x=-12\\\\\text{Answer:}\ x=-12;\ y=20\to\copyright\ (-12;\ 20)`

Answer 2

The first equation is 1x + 1y = 8, satisfied by all four answers.

The second equation is 2x+3y =36; checking we find

2(-12)+3(20) = -24+60 = 36

Choice C