Question

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

Answer 1

\[ \left[ \begin{array}{ccc}
-2 & -4 \\
3&2 \end{array} \right]\mathbf{x}= \left[ \begin{array}{ccc}
12 \\
2 \end{array} \right]\]

Where \(\textbf{x}=(x_1,x_2)\)

You see how I got this?

Answer 2

No. I don't get this at all.

Answer 3

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?

Answer 4

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

Answer 5

\[-2x–12=4y\\
2y+3x=2 \\[2ex]
-2x-4y=12\\
3x+2y=2\\[2ex]
\begin{bmatrix}
-2&-4\\3&2
\end{bmatrix}
\begin{bmatrix}
x\\y
\end{bmatrix}
=
\begin{bmatrix}
12\\2
\end{bmatrix}\]

Answer 6

My answer would be (12,2)?

Answer 7

no, answer is x, and y

Answer 8

How? Im so confused. It says to put my answer in as a ordered pair.

Answer 9

we have to use Cramer's rule to find (x,y)

Answer 10

Do you know what Cramer's rule is?

Answer 11

No thats what i am confused on

Answer 12

Cramer's rule says we can find (x, y), with determinants.

Do you know how to take the determinant of a matrix?

Answer 13

yes

Answer 14

What is the value of this determinant? \[D = \begin{vmatrix} -2&-4\\3&2\end{vmatrix}\]

Answer 15

8

Answer 16

good, that is D, the determinant of the coefficient matrix

Answer 17

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

Answer 18

32

Answer 19

And this one?\[D_y = \begin{vmatrix} -2&12\\3&2\end{vmatrix}\]

Answer 20

-32

Answer 21

try that one again

Answer 22

-40

Answer 23

ok, so we have found the values of the three determinants
D = 8,
D_x = 32,
D_y = -40.

Answer 24

so is my answer (32,-40)

Answer 25

Cramer's rule says that

x = D_x / D

y = D_y / D

Answer 26

(4,-5)

Answer 27

hmm, sounds about right, but lets check it

Answer 28

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?

Answer 29

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?

Answer 30

Yes they are both right

Answer 31

Woo hoo!

Then we have done it!

Answer 32

Thank you very much that helped so much.