Find values of x and y for given system of equations.

3x-2y=3
2x+2y=4

The given system of equations can be expressed in the form of AX=B,
?X=A^-1 B
A=\(\begin{bmatrix}3&-2\\2&2\end{bmatrix}\), X=\(\begin{bmatrix}x\\y\end{bmatrix}\), B=\(\begin{bmatrix}3\\4\end{bmatrix}\)
We know that, A^-1=\(\frac{1}{|A|}\) adj A
A^-1=\(\frac{1}{10} \begin{bmatrix}2&2\\-2&3\end{bmatrix}\)=\(\begin{bmatrix}\frac{1}{5}&\frac{1}{5}\\-\frac{1}{5}&\frac{3}{10}\end{bmatrix}\)
?X=A^-1 B=\(\begin{bmatrix}\frac{1}{5}&\frac{1}{5}\\-\frac{1}{5}&\frac{3}{10}\end{bmatrix}\begin{bmatrix}3\\4\end{bmatrix}\)=\(\begin{bmatrix}\frac{1}{5}×3+\frac{1}{5}×4\\-\frac{1}{5}×3+\frac{3}{10}×4\end{bmatrix}\)=\(\begin{bmatrix}\frac{7}{5}\\\frac{3}{5}\end{bmatrix}\)