SOLUTION: Use graphing to find the solutions to the system of equations. [ [ Y = x^2+7x+7 [ [ y = x+2 I tried to graph this, but it came out as an error.

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Question 668976: Use graphing to find the solutions to the system of equations.
[
[ Y = x^2+7x+7
[
[ y = x+2
I tried to graph this, but it came out as an error.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!

there's your graph.
the formula being graphed is:
x^2 + 7x + 7
and
x + 2
first intersection point is (-5,-3)
second intersection point is (-1,1)
it's hard to see on the graph but you can solve for it as well algebraically.
your 2 equations are:
y = x^2 + 7x + 7
y = x + 2
since both expressions on the right of the equal sign are equal to y, you can set them equal to each other to get:
x^2 + 7x + 7 = x + 2
subtract x and subtract 2 from both sides of the equation to get:
x^2 + 7x - x + 7 - 2 = 0
combine like terms to get:
x^2 + 6x + 5 = 0
factor this quadratic equation to get:
(x + 5) + (x + 1) = 0
solve for x to get:
x = -5
x = -1
substitute in either equation to solve for y.
when x = -5, y = x + 2 becomes y = -3
when x = -1, y = x + 2 becomes y = 1
that gets your your intersection points of (-5,-3) and (-1,1)
you can also substitute in the other equation to get the same answer.
example:
y = x^2 + 7x + 2 becomes y = (-5)^2 + 7(-5) + 7 which becomes y = 25 - 35 + 7 which becomes y = -10 + 7 which becomes y = -3