SOLUTION: Hello, I've been having trouble with Linear equations. Can you help me how to solve them step by step? Thanks y<x^2+1 y>-x^2+1 p.s: I need to Graph it too.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hello, I've been having trouble with Linear equations. Can you help me how to solve them step by step? Thanks y<x^2+1 y>-x^2+1 p.s: I need to Graph it too.      Log On


   



Question 695848: Hello, I've been having trouble with Linear equations. Can you help me how to solve them step by step? Thanks
y y>-x^2+1

p.s: I need to Graph it too.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Something went wrong (got lost in translation) while you were entering the problem. Maybe you had some typos.
Or maybe not everything you typed is shown the way you meant because of the way characters are coded by computers.
Linear equations (in their most simplified form) do not have exponents on the variables, and I see exponents, so maybe you meant non-linear.
Equations involve equal signs, but I see a > sign instead, which would make it an inequality instead of an equation.

Maybe you meant you have to solve, by graphing, the system of non-linear inequalities
system%28y%3Cx%5E2%2B1%2Cy%3E-x%5E2%2B1%29

y=x%5E2%2B1 is a non-linear equation. It can also be called a non-linear function.
Because the x is squared it can also be called a quadratic function.
The graph for the quadratic function y=x%5E2%2B1 is graph%28300%2C180%2C-5%2C5%2C-5%2C25%2Cx%5E2%2B1%29
graph%28300%2C180%2C-5%2C5%2C-25%2C5%2Cy=6%2C-x%5E2%2B1%29 is the graph of quadratic function y=x%5E2%2B1.
Graphing both together, you would have graph%28300%2C300%2C-5%2C5%2C-25%2C25%2Cx%5E2%2B1%2C-x%5E2%2B1%29
The graphs touch at the point where x=0 and y=1.

To graph y%3Cx%5E2%2B1 you would just
graph y=x%5E2%2B1 as a dotted line (to show that those points are not part of the solution),
and then you would color or shade the points (below the curve) that have smaller y values, to get something like this:
graph%28300%2C180%2C-5%2C5%2C-5%2C25%2Cy%3Cx%5E2%2B1%29

For y%3E-x%5E2%2B1, you would graph y=-x%5E2%2B1 as a dotted line,
and then you would color or shade the points (above the curve) that have larger y values, to get something like this:
graph%28300%2C180%2C-5%2C5%2C-25%2C5%2Cy%3E-x%5E2%2B1%29

To graph system%28y%3Cx%5E2%2B1%2Cy%3E-x%5E2%2B1%29 you would just graph both curves as dotted lines
(to show that those points are not part of the solution),
and then you would color or shade the points in between,
the ones that are part of the graph of y%3Cx%5E2%2B1
and also are part of the graph of y%3E-x%5E2%2B1