Two lines intersect to form a linear pair with equal measures. one angle had the measure 2x and the other angle had the measure (2y-10) find the value of x and y

From googling linear pair you we now that both angles add to 180.
2x + (2y - 10) = 180

You are missing out information since there are two unknowns, x and y. To solve two unknowns we need to equations. If you would like to comment what the other equation could be i.e. there could be another 'linear pair' rule that I don't know about - which is likely - I'd reply and solve it better for you.