Question

Solve the following system of equations using an inverse matrix. You must alsoindicate the inverse matrix, A-1, that was used to solve the system. You mayoptionally write the inverse matrix with a scalar coefficient.-x-6y = 8- 3x-10y = 6

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

`\begin{gathered} -x-6y=8 \\ -3x-10y=6 \end{gathered}`

STEP 2: Put the equation in a matrix form

`\begin{bmatrix}{-1} & {-6} \\ {-3} & {-10}\end{bmatrix}=\begin{bmatrix}{8} & {} \\ {6} & {}\end{bmatrix}`

STEP 3: Find the inverse

`A^(-1)=\begin{bmatrix}{(5)/(4)} & {(-3)/(4)} \\ {(-3)/(8)} & {(1)/(6)}\end{bmatrix}`

Hence, the answer to the image is given as:

`-8\begin{bmatrix}{-10} & {6} \\ {3} & {-1}\end{bmatrix}`

and the values of x and y are:

`\begin{gathered} x=(11)/(2) \\ y=-(9)/(4) \end{gathered}`