How do you solve the system of equations 4x ^ { 2} + 9y ^ { 2} = 724x2+9y2=72 and x ^ { 2} - y ^ { 2} = 5x2y2=5?

1 Answer
Jul 21, 2017

See below
x=+-3x=±3
y=+-2y=±2

Explanation:

To solve the system of equations 4x^2+9y^2=72 and x^2−y^2=54x2+9y2=72andx2y2=5, the easiest method is substitution.

I would solve the second equation for x^2x2
x^2−y^2=5" "rArr" "x^2=y^2+5x2y2=5 x2=y2+5

Substitute this into the first equation
4(y^2+5)+9y^2=724(y2+5)+9y2=72
4y^2+20+9y^2=724y2+20+9y2=72
combine to get: 13y^2+20=7213y2+20=72
subtract 2020 from both sides: 13y^2+20-20=72-2013y2+2020=7220
13y^2=5213y2=52
divide both sides by 13: (13y^2)/13=52/1313y213=5213
y^2=4y2=4
y=+-2y=±2

Substitute into the other equation
4x^2+9(4)=724x2+9(4)=72
4x^2=36" "x^2=94x2=36 x2=9
x=+-3x=±3