Posted by **Tom** on Friday, November 9, 2012 at 1:50pm.

help me solve this equation by substitution.

y^2− 4x^2 = 7

9y^2+16x^2 = 323

- Algebra -
**Reiny**, Friday, November 9, 2012 at 3:33pm
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

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