## anonymous one year ago 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

1. zzr0ck3r

$\left[ \begin{array}{ccc} -2 & -4 \\ 3&2 \end{array} \right]\mathbf{x}= \left[ \begin{array}{ccc} 12 \\ 2 \end{array} \right]$ Where $$\textbf{x}=(x_1,x_2)$$ You see how I got this?

2. anonymous

No. I don't get this at all.

3. anonymous

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?

4. anonymous

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

5. UnkleRhaukus

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

6. anonymous

7. UnkleRhaukus

no, answer is x, and y

8. anonymous

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

9. UnkleRhaukus

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

10. UnkleRhaukus

Do you know what Cramer's rule is?

11. anonymous

No thats what i am confused on

12. UnkleRhaukus

Cramer's rule says we can find (x, y), with determinants. Do you know how to take the determinant of a matrix?

13. anonymous

yes

14. UnkleRhaukus

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

15. anonymous

8

16. UnkleRhaukus

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

17. UnkleRhaukus

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

18. anonymous

32

19. UnkleRhaukus

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

20. anonymous

-32

21. UnkleRhaukus

try that one again

22. anonymous

-40

23. UnkleRhaukus

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

24. anonymous

25. UnkleRhaukus

Cramer's rule says that x = D_x / D y = D_y / D

26. anonymous

(4,-5)

27. UnkleRhaukus

hmm, sounds about right, but lets check it

28. UnkleRhaukus

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?

29. UnkleRhaukus

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?

30. anonymous

Yes they are both right

31. UnkleRhaukus

Woo hoo! Then we have done it!

32. anonymous

Thank you very much that helped so much.