2 Answers

Plannapus · Answer 1 · 2021-01-21T00:54:14+0000

Answer:

x=2 and
y=2

Explanation:

To use Cramer's Rule, we first need to turn this system of equations into a matrix

$A=\left[\begin{array}{cc}-1&-3\\2&4\\\end{array}\right]$ ,
$b=\left[\begin{array}{c}-8\\12\\\end{array}\right]$

The first step to use Cramer's Rule is to find the determinant of the original matrix

$detA=(4)(-1)-(2)(-3)\\\\detA=-4+6\\\\detA=2$

Next, we need to replace column 1 of matrix A with b and then find the determinant of that matrix

$A_1=\left[\begin{array}{cc}-8&-3\\12&4\\\end{array}\right]$

$detA_1=(-8)(4)-(12)(-3)\\\\detA_1=-32-(-36)\\\\detA_1=4$

And now we need to replace column 2 of matrix A with b and then find the determinant of that matrix

$A_2=\left[\begin{array}{cc}-1&-8\\2&12\\\end{array}\right]$

$detA_2=(-1)(12)-(2)(-8)\\\\detA_2=-12-(-16)\\\\detA_2=4$

Now that all of this is done, we can find the values for our x matrix.

Recall that Cramer's Rule states that

$x=\left[\begin{array}{c}(detA_1)/(detA) \\(detA_2)/(detA) \\\end{array}\right]$

Now that we know all of the required determinants, we can find x

$x=\left[\begin{array}{c}(4)/(2) &(4)/(2) \end{array}\right] \\\\x=\left[\begin{array}{c}2\\2\\\end{array}\right]$

This means that the solutions to this system are
x=2 and
y=2

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