We have to solve the system of equations by Cramer's rule.
The coefficient matrix is given by
[tex]D=\begin{bmatrix}3&4\\8 &-2\end{bmatrix}[/tex]
Let us find the determinant of coefficient matrix.
[tex]|D|= -6-32=-38[/tex]
For X-matrix
[tex]D_x=\begin{bmatrix}15&4\\40 & -2\end{bmatrix}[/tex]
Now, we find its determinant
[tex]|D_x|=-30-160=-190[/tex]
For Y-matrix
[tex]D_x=\begin{bmatrix}15&3\\ 40&8\end{bmatrix}[/tex]
Now, we find its determinant
[tex]|D_y|=120-120=0[/tex]
Therefore, the value for x is given by
[tex]x=\frac{D_x}{D}\\\\x=\frac{-190}{-38}\\\\x=5[/tex]
The value for x is 5.
