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

SOLUTION

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

$A^{-1}=\begin{bmatrix}{\frac{5}{4}} & {\frac{-3}{4}} \\ {\frac{-3}{8}} & {\frac{1}{6}}\end{bmatrix}$

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:

$\begin{gathered} x=\frac{11}{2} \\ y=-\frac{9}{4} \end{gathered}$