SOLUTION: Give 3 sets of points that satisfy the equations: 2x+2y=4 and y=x^2-4

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Question 152559: Give 3 sets of points that satisfy the equations:
2x+2y=4 and y=x^2-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Are you trying to solve this as a system? If you are, then there are two points that satisfy this system

2x%2B2y=4+ Start with the first equation.


2x%2B2%28x%5E2-4%29=4+ Plug in y=x%5E2-4


2x%2B2x%5E2-8=4+ Distribute


2x%2B2x%5E2-8-4=0 Get all terms to the left side.


2x%5E2%2B2x-12=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=2, and c=-12


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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%282%29%28-12%29+%29%29%2F%282%282%29%29 Plug in a=2, b=2, and c=-12


x+=+%28-2+%2B-+sqrt%28+4-4%282%29%28-12%29+%29%29%2F%282%282%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4--96+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-12%29 to get -96


x+=+%28-2+%2B-+sqrt%28+4%2B96+%29%29%2F%282%282%29%29 Rewrite sqrt%284--96%29 as sqrt%284%2B96%29


x+=+%28-2+%2B-+sqrt%28+100+%29%29%2F%282%282%29%29 Add 4 to 96 to get 100


x+=+%28-2+%2B-+sqrt%28+100+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-2+%2B-+10%29%2F%284%29 Take the square root of 100 to get 10.


x+=+%28-2+%2B+10%29%2F%284%29 or x+=+%28-2+-+10%29%2F%284%29 Break up the expression.


x+=+%288%29%2F%284%29 or x+=++%28-12%29%2F%284%29 Combine like terms.


x+=+2 or x+=+-3 Simplify.


So the answers are x+=+2 or x+=+-3


So the two solutions are (2,0) and (-3,5)