Answer:
0
Step-by-step explanation:
We find the determinant of a matrix by the method below. If we have a matrix:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
The determinant is [tex]ad-bc[/tex]
Now, using cramer's rule, we find x-value by the formula:
[tex]x=\frac{D_x}{D}[/tex]
Where D is the determinant of the original problem and [tex]D_x[/tex] 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 [tex]D_x[/tex], 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:
[tex]\left[\begin{array}{cc}3&4\\1&-6\end{array}\right] \\D=(3)(-6)-(1)(4)=-18-4=-22[/tex]
To get [tex]D_x[/tex]:
[tex]\left[\begin{array}{cc}12&4\\-18&-6\end{array}\right] \\D_x=(12)(-6)-(-18)(4)=0[/tex]
Putting into the formula, we get:
[tex]x=\frac{D_x}{D}=\frac{0}{-22}=0[/tex]
Thus, the value of x is 0
