Question 160343
-11x = 395 + y
14y = -634 - 10x 
:
Any method is tedious here, arrange the equations, thusly:
-11x -  y = 395
+10x +14y = -634
:
Multiply the 1st equation by 14
-154x - 14y = 5530
+ 10x + 14y = -634
---------------------addition eliminates y, find x
-144x + 0y = 4896
x = {{{4896/(-144)}}}
x = -34
:
Find y using the 2nd original equation
14y = -634 - 10(-34)
14y = -634 + 340
14y = -294
y = {{{(-294)/14}}}
y = -21
:
:
Check solutions in the 1st original equation:
-11x = 395 + y
-11(-34) = 395 + (-21)
+374 = 395 - 21
374 = 374; equality reigns