y + x = 5x + 3
12 - y = x + 2y
Isolate x in the first equation, then substitute its expression into the second equation to find y:
y + x = 5x + 3
x = 5x - y + 3
-4x = -y + 3
x = y - 3/4
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12 - y = x + 2y
12 - y = (y - 3/4) + 2y
48 - 4y = y - 3 + 8y
48 - 4y = 9y - 3
-4y = 9y -51
-13y = -51
y = 51/13
Substitute this into the first equation to find x:
51/13 + x = 5x + 3
x - 5x = 3 - 51/13
-4x = -12/13
x = 3/13
Lastly, substitute back into both original equations to check work;
y + x = 5x + 3 --> 51/13 + 3/13 = 5(3/13) + 3 --> 54/13 = 54/13
12 - y = x + 2y --> 12 - 51/13 = 3/13 + 2(51/13) --> 105/13 = 105/13
Answer:
x = 3/13
y = 51/13
Hope this helps.