Circles M and K are congruent, QR is congruent to LN and OP is congruent to
VW . Find x and y.

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- anonymous

Circles M and K are congruent, QR is congruent to LN and OP is congruent to
VW . Find x and y.

- schrodinger

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- anonymous

##### 1 Attachment

- dessyj1

Hi

- dessyj1

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

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## More answers

- 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.

- anonymous

how do we do that?

- dessyj1

Are you familiar with substitution and elimination?

- dessyj1

|dw:1439264950385:dw|

- dessyj1

|dw:1439265152284:dw|

- anonymous

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

- 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.

- anonymous

how do I do the other ones?

- 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).

- dessyj1

It does not matter which equation you pick.

- dessyj1

Can you do that?

- anonymous

how do I isolate the variable ?

- dessyj1

|dw:1439265518144:dw|

- dessyj1

Do you understand what I did?

- anonymous

yes!

- anonymous

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

- dessyj1

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

- dessyj1

We now have a one-variable equation.

- dessyj1

Which means we can solve for x (yay!)

- anonymous

|dw:1439266161322:dw|

- anonymous

??

- dessyj1

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

- dessyj1

the original equation was wrong.

- anonymous

I'm really confused

- dessyj1

I will now* solve for x.

- dessyj1

|dw:1439266535709:dw|

- anonymous

so x = 8?

- dessyj1

no i am not done.

- dessyj1

I have to completely isolate the x.

- dessyj1

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

- dessyj1

Sorry...

- dessyj1

The answer is x=4 and y=-1

- dessyj1

I just made too many mistakes with typing...

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