use substitution to find (x,y) where each pair of lines interesct.

y=-2+3(x-7)
y=10-5x

Since both 2 + 3(x - 7) and 10 - 5x are equal to y, and y = y obviously, set them equal to each other:

2 + 3(x - 7) = 10 - 5x

Solve this equation for x

Then plug the value obtained in to either 2 + 3(x - 7) or 10 - 5x to find y