Solve the following nonlinear systems of equations 1 x2y2625

Solve the following non-linear systems of equations.

1) x^2+y^2=625

3x-y=-25

2) x^3-y^2=23

2x-3y=0

please show all the steps

1. x^2+y^2=625 ----(1)

3x-y=-25 ----(2)

y = 3x +25 substitute in equation 1)

x^2 + (3x +25)^2 = 625

10x^2 +625 + 150x = 625

10x^2 +150x =0

x( 10x +150)=0

x =0 ; x = -15

y = 3x +25 = 25

y = 3(-15) +25 = -20

Solution: (x,y) = (0, 25) and ( -15 , -20)

x^3-y^2=23 ----(1)

2x-3y=0 ----(2)

Substitute y = 2x/3

x^3 - (2x/3)^2 =23

x^3 - 4x^2/9 = 23

9x^3 - 4x^2 -207 =0

on solving the cubic equation : x = 3; x = -1.27 +i*2.46

x = -1.27 - i*2.46

y = 2x/3 = 2

y = 2/3(-1.27 +/ - i*2.46