Question

Use Cramers Rule to solve the system -x-3y=-8 2x+4y=12

Answer 1

Answer:

$x=2$ and $y=2$

Step-by-step 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

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

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

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

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

Answer 2

Answer:

x = 2 y = 2

Step-by-step explanation:

just do equation form