## anonymous one year ago Circles M and K are congruent, QR is congruent to LN and OP is congruent to VW . Find x and y.

1. anonymous

2. dessyj1

Hi

3. dessyj1

Congruent means equal, so when they say QR is congruent to LN, they mean QR is equal to LN.

4. dessyj1

Since they want us to find x as well as y, and they give us two cases(LN=QR; OP=VW), it means we will probably have to use a system of equations.

5. anonymous

how do we do that?

6. dessyj1

Are you familiar with substitution and elimination?

7. dessyj1

|dw:1439264950385:dw|

8. dessyj1

|dw:1439265152284:dw|

9. anonymous

|dw:1439264918997:dw| I don't know... this is what I got ..

10. dessyj1

Elimination does not work with these equations. If it did you would be left with either just the x-variable in your answer or the y-variable in your answer, but not both at the same time.

11. anonymous

how do I do the other ones?

12. dessyj1

We have to use substitution. What we are going to do is pick one of the two original equations and completely isolate a variable. (either x or y will work).

13. dessyj1

It does not matter which equation you pick.

14. dessyj1

Can you do that?

15. anonymous

how do I isolate the variable ?

16. dessyj1

|dw:1439265518144:dw|

17. dessyj1

Do you understand what I did?

18. anonymous

yes!

19. anonymous

but would that be the answer? because it looks weird, and when I solved it (or attempted to) it was a decimal.

20. dessyj1

No. it is not. Okay, now we have to get the other equation and substitute y into it. Like so. |dw:1439265853745:dw|

21. dessyj1

We now have a one-variable equation.

22. dessyj1

Which means we can solve for x (yay!)

23. anonymous

|dw:1439266161322:dw|

24. anonymous

??

25. dessyj1

Not quite. And I made a mistake. the y isolation is supposed to be |dw:1439266307629:dw|

26. dessyj1

the original equation was wrong.

27. anonymous

I'm really confused

28. dessyj1

I will now* solve for x.

29. dessyj1

|dw:1439266535709:dw|

30. anonymous

so x = 8?

31. dessyj1

no i am not done.

32. dessyj1

I have to completely isolate the x.

33. dessyj1

Listen, can we start over? Because if I keep on going, I may further confuse you.

34. dessyj1

Sorry...

35. dessyj1

The answer is x=4 and y=-1

36. dessyj1

I just made too many mistakes with typing...