What are x and y if y=x^2+6x+2y=x2+6x+2 and y=-x^2+2x+8y=−x2+2x+8?

1 Answer
Roella W.
Dec 22, 2015

(1,9)(1,9) and (-3,-7)(−3,−7)

Explanation:

I interpret the question as asking what values of x and y will satisfy both expressions. In that case, we can say that for the required points
x^2 +6x +2 = -x^2 +2x +8x2+6x+2=−x2+2x+8
Moving all items to the left gives us
2x^2 +4x -6 = 02x2+4x−6=0
(2x -2)(x + 3) = 0(2x−2)(x+3)=0
Therefore x=1x=1 or x=-3x=−3
Substituting into one of the equations gives us
y = -(1)^2 +2*(1) +8 = 9y=−(1)2+2⋅(1)+8=9
or y = -(-3)^2 + 2*(-3) +8y=−(−3)2+2⋅(−3)+8
y = -9 -6 +8 = - 7y=−9−6+8=−7
Therefore the points of intersection of the two parabolas are (1,9)(1,9) and (-3,-7)#

Related questions
See all questions in Systems Using Substitution
Impact of this question
1316 views around the world
You can reuse this answer
Creative Commons License