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Solve equation????

Solve the nonlinear system of equation for real solution
 
5 x2 + 3 y2 = 120
 
-x+ y2  = 16
 
a) The solution is ???????
 
b)the is no solution
 

1 Answer by Expert Tutors

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Ron S. | Expert in Test Prep, Science, and MathExpert in Test Prep, Science, and Math
4.8 4.8 (51 lesson ratings) (51)
1
There are four; the first equation is an ellipse, and the second is a hyperbola that intercepts the ellipse at (±3, ±5). Try substitution as follows:
 
y2 = 16 + x2, so 5x2 + 3(16 + x2) = 120 and solve as
 
5x2 + 48 + 3x2 = 120
8x2 = 120 - 48
x2 = 72/8 = 9 so x = ±3
 
either of these values plugged into the second equation yields y2 = 16 + 9 = 25 so y = ±5
 
the full set would be (-3, -5), (-3, 5), (3, -5), (3, 5)
 
Good Luck!