1/2x+1/3y=5 ----- (1)
1/4x+y=10 -------- (2)
From (2), y = 10 - (1/4)x. Sibstitute for this into (1), to give
(1/2)x + (1/3)(10 - (1/4)x) = 5
(1/2)x + 10/3 - (1/12)x = 5
(1/2 - 1/12)x = 15/3 - 10/3
(5/12)x = 5/3
x = (5/3)(12/5) = 4
x = 4
y = 10 - (1/4)x = 10 - 1
y = 9