Question

solve the nonlinear system of equation 3y^2-5x^2=7 and 6y^2-7x^2=26

Answer 1

\[ 3y^2-5x^2=7\]\[6y^2-7x^2=26\]multiply the first equation by -2 and add it to the second, then solve for x.
use what you get for x to find y

Answer 2

3y^2 -5x^2 =7
6y^2 -7x^2 =26 ---- 6y^2 =7x^2 +26 ---- y^2 =(7x^2 +26)/6

3(7x^2 +26)/6 -5x^2 =7
(7x^2 +26)/2 -5x^2 =7
7x^2 +26 -10x^2 =14
-3x^2 =-12
3x^2 =12
x^2 = 12/3 =4
x_1,2 = +/- sqrt4 = +/- 2

y^2 =(7*4^2 +26)/6 =(7*16 +26)/6 =(112 +26)/6 = 138/6 =23
y_1,2=+/- sqrt23

x_1,2= +/- 2
y_1,2= +/- sqrt23