x + y = 3 subtract x from both sides to get y = 3 - x
x2 + y2 = 9 Substitute 3 - x for y in this equation.
x2 + (3 - x)2 = 9 Now we can solve this for x .
x2 + (3 - x)(3 - x) = 9
x2 + 9 - 6x + x2 = 9 Subtract 9 from both sides and combine like terms.
2x2 - 6x = 0 Factor x out of both terms on the left side.
x(2x - 6) = 0 Set each factor equal to zero.
x = 0 or 2x - 6 = 0
x = 3
Now we can use these values for x to find y .
If x = 0 , 0 + y = 3 so y = 3
If x = 3 , 3 + y = 3 so y = 0
The solutions are (0, 3) and (3, 0) .