In the system shown below, what is the sum of the x-coordinates of all solutions?

3y^2-5x^2=7

3y^2-x^2=23

We are given the equation 3y^2-5x^2=7 and 3y^2-x^2=23. there are two equations two unknowns hence the problem can be solved.

3y^2-5x^2=7

3y^2 = x^2 + 23

x^2 + 23 = 7 + 5x^2

4x^2 = 16

x^2 = 4

x1 = 2

x2 = - 2

sum is 2-2 = 0