Algebra
posted by Tom on .
help me solve this equation by substitution.
y^2− 4x^2 = 7
9y^2+16x^2 = 323

from the 1st: y^2 = 4x^2 + 7
into the 2nd
9(4x^2 + 7) + 16x^2 = 323
36x^2 + 63 + 16y^2 = 323
52y^2 = 260
y^2 = 5
y = ± √5
sub y^2 = 5 into the 1st:
5  4x^2 = 7
4x^2 = 2
x^2 = 1/2
x = ± 1/√2
4 solutions:
x=√5, y= 1/√2
x = √5, y = 1/√2
x = √5, y = 1/√2
x = √5 , y = 1/√2
your graph would show an ellipse intersecting with a hyperbola, with 4 symmetric points of intersection