Can you please help me solve these problems? Thank You

Question

1.x^2-y^2=25
x^2+y^2+7=0

2. x^2+y^2=8
5y^2=3x^2

3. 3x^2-2y^2=24
2y=-3x

Answer 1

#1
add the two equations to eliminate y^2:
2x^2=18
x = ±3

#2 multiply by 3 to get
3x^2+3y^2=24
since 3x^2 = 5y^2,
8y^2 = 24
y^2 = 3

#3
just sub in directly:
3x^2-2y^2 = 24
3x^2 - (1/2)(2y)^2 = 24
3x^2 - (1/2)(3x)^2 = 24
6x^2 + 9x^2 = 48
15x^2 = 48
x^2 = 16/5