To solve this system of equations, we can add the two equations together to eliminate the y^2 terms:
X^2 + y^2 + x^2 - y^2 = 61 + 112x^2 = 72x^2 = 36x = 6 or x = -6
Now we can substitute the value of x back into one of the equations to solve for y:
For x = 6:6^2 + y^2 = 6136 + y^2 = 61y^2 = 25y = 5 or y = -5
So the solutions to the system of equations are:x = 6, y = 5x = 6, y = -5x = -6, y = 5x = -6, y = -5
To solve this system of equations, we can add the two equations together to eliminate the y^2 terms:
X^2 + y^2 + x^2 - y^2 = 61 + 11
2x^2 = 72
x^2 = 36
x = 6 or x = -6
Now we can substitute the value of x back into one of the equations to solve for y:
For x = 6:
6^2 + y^2 = 61
36 + y^2 = 61
y^2 = 25
y = 5 or y = -5
So the solutions to the system of equations are:
x = 6, y = 5
x = 6, y = -5
x = -6, y = 5
x = -6, y = -5