SOLUTION: Y=x^2+2x-3 Y=2x+1 Need help with this question please Thank you

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Question 968090: Y=x^2+2x-3
Y=2x+1
Need help with this question please
Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x%2B1 is a linear equation. Its graph is a straight line.
y=x%5E2%2B2x-3 is not a linear equation.
It is an equation of degree 2 (the greatest exponent),
and we call it a quadratic equation.
Quadratic functions like y=x%5E2%2B2x-3 graph as parabolas,
and this one looks like graph%28300%2C500%2C-6%2C6%2C-5%2C15%2Cx%5E2%2B2x-3%29 .
The two function graphed together look like this:
graph%28300%2C500%2C-6%2C6%2C-5%2C15%2Cx%5E2%2B2x-3%2C2x%2B1%29 .
It is easy to see that there will be two answers:
the two pairs of coordinates of the intersection points.
Let's find them.
There are, and there will be two equations,
but we can combine them so as to get an equation with no y ,
and replace the combination for one of the equations,
We can easily combine them by substituting
the expression 2x%2B1 for y
in the equation that is not y=2x%2B1 .
We can keep the simpler equation y=2x%2B1 ,
and substitute the combination for the other one.
system%28y=2x%2B1%2Cy=x%5E2%2B2x-3%29--->system%28y=2x%2B1%2C2x%2B1=x%5E2%2B2x-3%29
Now we solve the equation in x (no y )
2x%2B1=x%5E2%2B2x-3
2x%2B1-2x-1=x%5E2%2B2x-3-2x-1
0=x%5E2-4
0%2B4=x%5E2-4%2B4
4=x%5E2
There are two solutions for x : system%28x=2%2C%22or%22%2Cx=-2%29 ,
and for each of them, there will be a corresponding y%7D%7D+value%2C+given+by+%7B%7B%7By=2x%2B1 .
For x=2 :
system%28y=2x%2B1%2Cx=2%29-->system%28y=2%2A2%2B1%2Cx=2%29-->system%28y=4%2B1%2Cx=2%29-->highlight%28system%28y=5%2Cx=2%29%29
For x=-2 :
system%28y=2x%2B1%2Cx=2%29-->system%28y=2%2A%28-2%29%2B1%2Cx=2%29-->system%28y=-4%2B1%2Cx=2%29-->highlight%28system%28y=-3%2Cx=2%29%29