Question

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

Answer 1

Answer:

0

Step-by-step explanation:

We find the determinant of a matrix by the method below. If we have a matrix:

$\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

The determinant is $ad-bc$

Now, using cramer's rule, we find x-value by the formula:

$x=\frac{D_x}{D}$

Where D is the determinant of the original problem and $D_x$ is the determinant of the x-value matrix. How do we get those?

To get original matrix and thus D, we set up the matrix as the coefficients of x and y (s) of both the equations and to get matrix of x-value and thus $D_x$, we replace the x values of the matrix with the numbers in the right hand side of the 2 equations. We show this below:

To get D:

$\left[\begin{array}{cc}3&4\\1&-6\end{array}\right] \\D=(3)(-6)-(1)(4)=-18-4=-22$

To get $D_x$:

$\left[\begin{array}{cc}12&4\\-18&-6\end{array}\right] \\D_x=(12)(-6)-(-18)(4)=0$

Putting into the formula, we get:

$x=\frac{D_x}{D}=\frac{0}{-22}=0$

Thus, the value of x is 0