# Thread: System of second degree equations and inequalities?

1. ## System of second degree equations and inequalities?

Can anyone help me answer these two questions?

1. Find the coordinates of the point of intersection for the graphs
x^2=25-9y^2
xy=-4

I am slightly confused on how I would find x and y

The second question is graph each system of linear inequalities

x^2+4y less than 16

x^2 less than y^2+4

What I do not understand in this question is how I could get it to y=mx+b

Because whenever I move it I end up getting a negative?

2. Originally Posted by homeylova223
Can anyone help me answer these two questions?

1. Find the coordinates of the point of intersection for the graphs
x^2=25-9y^2
xy=-4

I am slightly confused on how I would find x and y
From xy= -4 you get y= -4/x. Put that into the first equation: x^2= 25- 144/x^2. Multiply through by x^2: x^4= 25x^2- 144 which is the same as x^4- 25x^2+ 144= 0. Let u= x^2 so the equation becomes u^2- 25u+ 144= 0. Solve that for two values of u. Solve x^2= u for each of those values of u to find four values of x. Finally, solve y= -4/x for each value of x to get four (x, y) pairs.

The second question is graph each system of linear inequalities

x^2+4y less than 16

x^2 less than y^2+4

What I do not understand in this question is how I could get it to y=mx+b
You can't! Why would you think you could? y= mx+ b is linear and equations involving x^2 are not- their graphs are parabolas.

Because whenever I move it I end up getting a negative?
What's do you mean? What's wrong with negtives?

The best way to solve an inequality is to start by solving the equation.
$\displaystyle x^2+ 4y= 16$ is the same as $\displaystyle 4y= 16- x^2$ or $\displaystyle y= 4- x^2/4$. That's a parabola, opening downward, with vertex at (0, 4), and symmetric about the y-axis. Graph that parabola. The point is that "x^2+ 4y= 16" separates "x^2+ 4y> 16" from "x^2+ 4y< 16". That parabola separates the plane into two parts, one which satisfies x^2+ 4y> 16 and the other x^2+ 4y< 16. I see that (0, 0) (which is below the parabola) satisfies 0^2+ 4(0)= 0< 16 so every point below the parabola satisfies x^2+ 4y< 16 and every point above it satisfies x^2+ 4y> 16.

3. I made an error when typing the problem I mean
x^2+4y^2 less than 16

I am sorry.

4. Again, start by graphing the equality: what does the graph of $\displaystyle x^2+ 4y^2= 16$ look like? (It is the same as $\displaystyle \frac{x^2}{16}+ \frac{y^2}{4}= 1$.)

As before points on that graph separate "> 16" from "< 16". Which points satisfy "< 16"?