Answer:
[tex]x=2[/tex] and [tex]y=2[/tex]
Step-by-step explanation:
To use Cramer's Rule, we first need to turn this system of equations into a matrix
[tex]A=\left[\begin{array}{cc}-1&-3\\2&4\\\end{array}\right][/tex] , [tex]b=\left[\begin{array}{c}-8\\12\\\end{array}\right][/tex]
The first step to use Cramer's Rule is to find the determinant of the original matrix
[tex]detA=(4)(-1)-(2)(-3)\\\\detA=-4+6\\\\detA=2[/tex]
Next, we need to replace column 1 of matrix A with b and then find the determinant of that matrix
[tex]A_1=\left[\begin{array}{cc}-8&-3\\12&4\\\end{array}\right][/tex]
[tex]detA_1=(-8)(4)-(12)(-3)\\\\detA_1=-32-(-36)\\\\detA_1=4[/tex]
And now we need to replace column 2 of matrix A with b and then find the determinant of that matrix
[tex]A_2=\left[\begin{array}{cc}-1&-8\\2&12\\\end{array}\right][/tex]
[tex]detA_2=(-1)(12)-(2)(-8)\\\\detA_2=-12-(-16)\\\\detA_2=4[/tex]
Now that all of this is done, we can find the values for our x matrix.
Recall that Cramer's Rule states that
[tex]x=\left[\begin{array}{c}\frac{detA_1}{detA} \\\frac{detA_2}{detA} \\\end{array}\right][/tex]
Now that we know all of the required determinants, we can find x
[tex]x=\left[\begin{array}{c}\frac{4}{2} &\frac{4}{2} \end{array}\right] \\\\x=\left[\begin{array}{c}2\\2\\\end{array}\right][/tex]
This means that the solutions to this system are [tex]x=2[/tex] and [tex]y=2[/tex]
