SOLUTION: what are all ordered pairs of a numbers (x,Y) which satisfy both x(x+y)=9 and y(x+y)=16

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Question 221114: what are all ordered pairs of a numbers (x,Y) which satisfy both x(x+y)=9 and y(x+y)=16
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
what are all ordered pairs of a numbers (x,Y) which satisfy both x(x+y)=9 and y(x+y)=16

Step 1. x%28x%2By%29=9 or x%5E2%2Bxy=9. Solving for xy=9-x%5E2

Step 2. y%28x%2By%29=xy%2By%5E2=16.

Step 3. Substitute xy from Step 1 into Step 2

9-x%5E2%2By%5E2=16

-x%5E2%2By%5E2=7 after subtracting 9 from both sides of the equation

Step 4. Now in Step 1, x%2By=9%2Fx and substitute into Step 2 to yield

y%2A9%2Fx=16 or y=16x%2F9

Step 5. Substitute y=16x%2F9 into Step 3.

-x%5E2%2B%2816x%2F9%29%5E2=7

-x%5E2%2B256x%5E2%2F81=7

Step 6. Multiply 9%5E2=81 to both sides to get rid of denominator

-81x%5E2%2B256x%5E2=81%2A7=567

175x%5E2=567

x=1.8 or x=-1.8

y=16%2A1.8%2F9=3.2 or y=-3.2

Step 7. The ordered pairs are (1.8, 3.2) and (-1.8, -3.2).

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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