Question

Rewrite the matrix equation as a system of equations in standard form.

Answer 1

Given

`\begin{bmatrix}3 & {-1} \\ {1} & {2}\end{bmatrix}\begin{pmatrix}x \\ \:y\end{pmatrix}=\begin{pmatrix}8 \\ \:5\end{pmatrix}`

Step-by-step explanation

From the above, the equation can be rewritten as

`\begin{gathered} 3*1-1* y=8 \\ 1* x+2* y=5 \\ \begin{pmatrix}3x-y \\ x+2y\end{pmatrix}=\begin{pmatrix}8 \\ 5\end{pmatrix} \\ isolate\text{ x in eqn 1} \\ \mathrm{Substitute\:}x=(8+y)/(3) \\ \begin{bmatrix}(8+y)/(3)+2y=5\end{bmatrix} \\ 8+y+6y=15 \\ 7y=15-8 \\ 7y=7 \\ y=(7)/(7) \\ y=1 \\ \mathrm{For\:}x=(8+y)/(3)\text{ substitute y=1} \\ x=(8+1)/(3) \\ x=(9)/(3) \\ x=3 \end{gathered}`

Answer: Option A