Please Help! Immediately! Use Cramer's Rule to solve this system of equations. Write your answer as an ordered pair, like this (-4, 13) {−2x–12=4y 2y+3x=2

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Please Help! Immediately! Use Cramer's Rule to solve this system of equations. Write your answer as an ordered pair, like this (-4, 13) {−2x–12=4y 2y+3x=2

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\[ \left[ \begin{array}{ccc} -2 & -4 \\ 3&2 \end{array} \right]\mathbf{x}= \left[ \begin{array}{ccc} 12 \\ 2 \end{array} \right]\] Where \(\textbf{x}=(x_1,x_2)\) You see how I got this?
No. I don't get this at all.
Im behind in school and i couldn't figure out that problem i tried working it out but im running out of time. I appreciate you helping. Is (12,2) the answer?

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Could i get help with this one as well. Use Cramer's Rule to find the solution to this system of equations. Enter your answer as an ordered pair, like this: (-2, 14) {5x+8y=7 3x+10y=−1
\[-2x–12=4y\\ 2y+3x=2 \\[2ex] -2x-4y=12\\ 3x+2y=2\\[2ex] \begin{bmatrix} -2&-4\\3&2 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 12\\2 \end{bmatrix}\]
My answer would be (12,2)?
no, answer is x, and y
How? Im so confused. It says to put my answer in as a ordered pair.
we have to use Cramer's rule to find (x,y)
Do you know what Cramer's rule is?
No thats what i am confused on
Cramer's rule says we can find (x, y), with determinants. Do you know how to take the determinant of a matrix?
yes
What is the value of this determinant? \[D = \begin{vmatrix} -2&-4\\3&2\end{vmatrix}\]
8
good, that is D, the determinant of the coefficient matrix
Switching the first column and the solution column, we get \[D_x = \begin{vmatrix} 12&-4\\2&2\end{vmatrix}\] what is the value of this determinant
32
And this one?\[D_y = \begin{vmatrix} -2&12\\3&2\end{vmatrix}\]
-32
try that one again
-40
ok, so we have found the values of the three determinants D = 8, D_x = 32, D_y = -40.
so is my answer (32,-40)
Cramer's rule says that x = D_x / D y = D_y / D
(4,-5)
hmm, sounds about right, but lets check it
the first equation we were given is -2x-12 = 4y if (4,-5) is the solution, then -2(4)-12 = 4(-5) is a true statement, is this right?
The second equation was 2y+3x = 2 if (4,-5) is the solution, then 2(-5)+3(4) = 2 is also true. is this also right?
Yes they are both right
Woo hoo! Then we have done it!
Thank you very much that helped so much.

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