You are given a system of two equations

 = ,    (1)
 = .        (2)

Since their left sides are identical, you can equate their right sides. Then you will get an equation

 = .

(Notice: it is the same as to substitute expression (2) into equation (1)).

Simplify:

 = .

Factor the left side polynomial. You will get

x*(x-6) = 0.

It has two roots: x=0 and x=6.
The corresponding y's are (from (2)):  y = 2x+10 = 2*0+10 = 10  and  y = 2*6+10 = 22, correspondingly.

Answer. There are two solutions: 1) (x,y) = (0,10)  and  2) (x,y) = (6,22).