Solve 2x23y235 x2y25Solution2x23y2351 x2y25 x2y252 substitut

Solve:

2x^2+3y^2=35

x^2-y^2=-5

2x^2+3y^2=35-------->(1)

x^2-y^2=-5 ==>x^2=y^2-5------>(2)

substitute (2)in (1)

2(y^2-5)+3y^2=35

2y^2-10+3y^2=35

5y^2=35+10

5y^2=45

y^2=45/5

y^2=9

y =-3 , y =3

put y =-3 in x^2=y^2-5

x^2=(-3)^2-5

x^2=9-5

x^2=4

x=-2, x =2

put y =3 in x^2=y^2-5

x^2=(3)^2-5

x^2=9-5

x^2=4

x=-2, x =2

so thre solutions are (x,y)=(-2,-3),(2,-3),(-2,3),(2,3)