# Solve the simultaneous Linear equations using matrix inverse Method. 8x+3y=2 6x+2y=4

Solve the simultaneous Linear equations using matrix inverse Method.
8x+3y=2
6x+2y=4
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Step 1
To solve simultaneous linear equations, we have to find to form the equations into three matrices.
8x+3y=2
6x+2y=4
These can be shown in matrix form as,
$\left[\begin{array}{cc}8& 3\\ 6& 2\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}2\\ 4\end{array}\right]$
Step 2
So if Ax=B , where A,x and B are matrices.
Then we can multiply it with ${A}^{-1}$ to find x
${A}^{-1}\cdot Ax={A}^{-1}\cdot B⇒x={A}^{-1}B$
So find ${A}^{-1},A=\left[\begin{array}{cc}8& 3\\ 6& 2\end{array}\right],x=\left[\begin{array}{c}x\\ y\end{array}\right],B=\left[\begin{array}{c}2\\ 4\end{array}\right]$
,

Applying these row operations we get,

Step 3
${A}^{-1}AX={A}^{-1}B⇒x={A}^{-1}B$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{cc}-1& \frac{3}{2}\\ 3& -4\end{array}\right]\left[\begin{array}{c}2\\ 4\end{array}\right]$
$\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}-2+\frac{3}{2}×4\\ 6+-4×4\end{array}\right]=\left[\begin{array}{c}-2+6\\ 6-16\end{array}\right]=\left[\begin{array}{c}4\\ -10\end{array}\right]$

x=5 , y=-10
Step 4
So the answers are x = 4 and y = -10

Jeffrey Jordon