Question

Using Cramer’s Rule, what is the value of x in the system of linear equations below?

Answer 1

We have to solve the system of equations by Cramer's rule.

The coefficient matrix is given by

$D=\begin{bmatrix}3&4\\8 &-2\end{bmatrix}$

Let us find the determinant of coefficient matrix.

$|D|= -6-32=-38$

For X-matrix

$D_x=\begin{bmatrix}15&4\\40 & -2\end{bmatrix}$

Now, we find its determinant

$|D_x|=-30-160=-190$

For Y-matrix

$D_x=\begin{bmatrix}15&3\\ 40&8\end{bmatrix}$

Now, we find its determinant

$|D_y|=120-120=0$

Therefore, the value for x is given by

$x=\frac{D_x}{D}\\\\x=\frac{-190}{-38}\\\\x=5$

The value for x is 5.