Write the given matrix equation as a system of linear equations without matrices. begin{bmatrix}3 & 0 -3 &1 end{bmatrix}begin{bmatrix}x y end{bmatrix}=begin{bmatrix}6 -7 end{bmatrix}

Write the given matrix equation as a system of linear equations without matrices. $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$
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Step 1
Given: $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$
Step 2
Now, $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

From equation (1) , we have
$⇒3x=6$
$⇒x=\frac{6}{3}$
$⇒x=3$
Putting x=2 in equation (2) , we have
$-3\left(2\right)+1y=7$
$⇒-6+y=7$
$⇒y=7+6$
$⇒y=13$
Answer: Therefore the values of x and y are 2 and 13 respectively
Jeffrey Jordon