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

1 Answer
Jul 21, 2017

See below
#x=+-3#
#y=+-2#

Explanation:

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

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

Substitute this into the first equation
#4(y^2+5)+9y^2=72#
#4y^2+20+9y^2=72#
combine to get: #13y^2+20=72#
subtract #20# from both sides: #13y^2+20-20=72-20#
#13y^2=52#
divide both sides by 13: #(13y^2)/13=52/13#
#y^2=4#
#y=+-2#

Substitute into the other equation
#4x^2+9(4)=72#
#4x^2=36" "x^2=9#
#x=+-3#