anonymous
  • anonymous
Circles M and K are congruent, QR is congruent to LN and OP is congruent to VW . Find x and y.
Mathematics
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anonymous
  • anonymous
Circles M and K are congruent, QR is congruent to LN and OP is congruent to VW . Find x and y.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
dessyj1
  • dessyj1
Hi
dessyj1
  • dessyj1
Congruent means equal, so when they say QR is congruent to LN, they mean QR is equal to LN.

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dessyj1
  • 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
  • anonymous
how do we do that?
dessyj1
  • dessyj1
Are you familiar with substitution and elimination?
dessyj1
  • dessyj1
|dw:1439264950385:dw|
dessyj1
  • dessyj1
|dw:1439265152284:dw|
anonymous
  • anonymous
|dw:1439264918997:dw| I don't know... this is what I got ..
dessyj1
  • 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
  • anonymous
how do I do the other ones?
dessyj1
  • 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
  • dessyj1
It does not matter which equation you pick.
dessyj1
  • dessyj1
Can you do that?
anonymous
  • anonymous
how do I isolate the variable ?
dessyj1
  • dessyj1
|dw:1439265518144:dw|
dessyj1
  • dessyj1
Do you understand what I did?
anonymous
  • anonymous
yes!
anonymous
  • anonymous
but would that be the answer? because it looks weird, and when I solved it (or attempted to) it was a decimal.
dessyj1
  • 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
  • dessyj1
We now have a one-variable equation.
dessyj1
  • dessyj1
Which means we can solve for x (yay!)
anonymous
  • anonymous
|dw:1439266161322:dw|
anonymous
  • anonymous
??
dessyj1
  • dessyj1
Not quite. And I made a mistake. the y isolation is supposed to be |dw:1439266307629:dw|
dessyj1
  • dessyj1
the original equation was wrong.
anonymous
  • anonymous
I'm really confused
dessyj1
  • dessyj1
I will now* solve for x.
dessyj1
  • dessyj1
|dw:1439266535709:dw|
anonymous
  • anonymous
so x = 8?
dessyj1
  • dessyj1
no i am not done.
dessyj1
  • dessyj1
I have to completely isolate the x.
dessyj1
  • dessyj1
Listen, can we start over? Because if I keep on going, I may further confuse you.
dessyj1
  • dessyj1
Sorry...
dessyj1
  • dessyj1
The answer is x=4 and y=-1
dessyj1
  • dessyj1
I just made too many mistakes with typing...

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