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?
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.Originally Posted by homeylova223
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.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
What's do you mean? What's wrong with negtives?Because whenever I move it I end up getting a negative?
The best way to solve an inequality is to start by solving the equation.
is the same as
or
. 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.
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