Question

solve the following system or show that it has no solutions
x+2y=7
-2x+y=1
x-y=-2
3x+y=6

Answer 1

Solution. Start with the first, x = -2y + 7, so from the second equation one gets 4y - 14 + y = 1 or y = 3 and, hence x = 1.To conclude, the solution is
(1; 3).
Proceed with the second, x = -2+y, the second equation implies -6+3y+y = 6,
thus y = 3 and x = 1. The solution is (1; 3).
Solution. (1; 3), (1; 3)