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# Solve for x and y:$x\begin{bmatrix}2\\1\end{bmatrix}+y\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0$

Toolbox:
• The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywise: $(A (+/-) B)_{i,j} = A_{i,j} +/- B_{i,j}$ where 1 ≤ i ≤ m and 1 ≤ j ≤ n.
Step1:
Given:
$\begin{bmatrix}2x\\x\end{bmatrix}+\begin{bmatrix}3y\\5y\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0$
On adding the above matrices we get
2x+3y+(-8)=0.
2x+3y-8=0-----(1)
x+5y-11=0
x+5y=11-----(2)
2x+3y=8------(3)
Step2:
Multiply equation (2) by 2
2x+10y=22------(4)
Subtracting equation (4) from (3)
2x+3y=8
2x+10y=22
__________________
-7y=-14
7y=14.
y=2.
Step3:
Substitute the value of y in equation (2)
x+5y=11
x+5(2)=11.
x+10=11
x=11-10
x=1.