## anonymous 4 years ago Use Cramer's rule to solve the system of equations. { 2x+3y=4 x-2y=9

1. anonymous

Are you studying matrices / linear algebra?

2. anonymous

yes!

3. anonymous

Great, so how far have you got until now?

4. anonymous

(If you're stuck from the beginning, that's fine too though!)

5. anonymous

i understand how to do it, just the last step is where i mess up. I only know how to put them into the matrix sets, and solve those out. but i have no idea where to go from there.

6. anonymous

As I remember it, you create a square matrix A (left hand side of the equation) and column (that's vertical) vector b (right side of the equation). To get x, you replace the first column of your square matrix with vector b, whereas for y you replace the second column of your square matrix with vector b instead. In both cases, you then take the determinant of the new matrix you've created, and divide by the determinant of the original square matrix A. Does that make sense?

7. anonymous

If so, we can try it with the numbers now?

8. anonymous

If that doesn't make sense, we can do it using Draw.

9. anonymous

$\left[\begin{matrix}2 & 3 \\ 1 & -2\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right)=\left(\begin{matrix}4 \\ 9\end{matrix}\right)$

10. anonymous

yea i understand,

11. anonymous

Thanks iven5880!

12. anonymous

I'm still working on it. I'm not goot at using this editor

13. anonymous

So the original square matrix is the one that iven5880 has laid out, and whose determinant is 2*-2 -3*1 = -4-3=-7.

14. anonymous

|dw:1327953451141:dw|

15. anonymous

Awesome!

16. anonymous

arricuhh, does that part make sense to you?

17. anonymous

*airricuhh

18. anonymous

So x = -35/-7 = 5

19. anonymous

yea, i understand (:

20. anonymous

Can you do the same thing for y?

21. anonymous

can you help me with me it /:

22. anonymous

OK, how are you going to start?

23. anonymous

|dw:1327953694308:dw|

24. anonymous

So y = 14/-7 = 2

25. anonymous

oh, welll.. thank you iven5880! and thank you BasketWeave

26. anonymous

You're welcome! Mostly thanks to iven5880 though, I'd say :D

27. anonymous

:))

28. anonymous