nonlinear system help please?
X^2 +Y^2 = 9
(X^2/64) + (Y^2/16) = 1
EXPLAIN HOW TO SOLVE THIS ALGEBRAICALLY, i have no idea what your talking about if you're using a graph.
Update:its is x squared over 64 and y squared over 16 not a fractional exponent.
Comments
You can solve the first equation for y² in terms of x² (or the other way around) and reduce the system to a quadratic in a single variable.
y² = 9 - x².
Put this into the second equation
x²/64 + (9 - x²)/16 = 1.
Multiply through by 64 and collect like terms to get
x² + 4(9 - x²) = 64 ==> -3x² + 36 = 64 ==> 3x² = - 28.
There are no real solutions. If you are interested in complex solutions, then you can write x = ± i √(28/3) and find the corresponding y-values.
The first would have a graph that is a circle of radius 3 centered at the origin. The second would have a graph that is an ellipse with semi axes of lengths 8 and 4. The circle lies entirely inside of the ellipse, so there are no intersections.
the first equation is a circle with radius of 3 centered on the origin
rewrite the second as x^2 + 4y^2 = 64
when x = 0, y = 4 or -4
when y = 0, x = 8 or -8
this indicates that the ellipse surrounds the circle, and they do not intersect