SOLUTION: Can you help me solve this system algabraically and support the solutions graphically? y+x^2 9x-y=20 (ordered pairs)

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Question 151297: Can you help me solve this system algabraically and support the solutions graphically?
y+x^2
9x-y=20
(ordered pairs)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
What is y%2Bx%5E2 equal to? This is not an equation.


Did you mean to say y=x%5E2 ??


9x-y=20 Start with the second equation.


9x-x%5E2=20 Plug in y=x%5E2


9x-x%5E2-20=0 Subtract 20 from both sides.


-x%5E2%2B9x-20=0 Rearrange the terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-1, b=9, and c=-20


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%289%29+%2B-+sqrt%28+%289%29%5E2-4%28-1%29%28-20%29+%29%29%2F%282%28-1%29%29 Plug in a=-1, b=9, and c=-20


x+=+%28-9+%2B-+sqrt%28+81-4%28-1%29%28-20%29+%29%29%2F%282%28-1%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81-80+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-20%29 to get 80


x+=+%28-9+%2B-+sqrt%28+1+%29%29%2F%282%28-1%29%29 Subtract 80 from 81 to get 1


x+=+%28-9+%2B-+sqrt%28+1+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-9+%2B-+1%29%2F%28-2%29 Take the square root of 1 to get 1.


x+=+%28-9+%2B+1%29%2F%28-2%29 or x+=+%28-9+-+1%29%2F%28-2%29 Break up the expression.


x+=+%28-8%29%2F%28-2%29 or x+=++%28-10%29%2F%28-2%29 Combine like terms.


x+=+4 or x+=+5 Simplify.


So the x answers are x+=+4 or x+=+5


y=x%5E2 Go back to the first equation


y=4%5E2 Plug in x+=+4


y=16 Square 4 to get 16.


So the first set of answers is x+=+4 and y=16 which form the ordered pair (4,16)


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y=x%5E2 Go back to the first equation


y=5%5E2 Plug in x+=+5


y=25 Square 5 to get 25.


So the second set of answers is x+=+5 and y=25 which form the ordered pair (5,25)

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Answer:

So the ordered pair solutions are (4,16) and (5,25)


Notice that if we graph the two equations, we get



Graph of y=x%5E2 (red) and 9x-y=20 (green).


It's hard to see, but with the help of a graphing calculator, we can see that the graphs intersect at the points (4,16) and (5,25). So this verifies our answer.