Question 479974
9x+5y=2 ……….(1)
-11x+2y=-27…………(2)

Multiply (1) by 2 and (2) by (-5) then add both equations.
18x+10=4
55x-10y=135
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73x=139
x=139/73

Put the value of x in equation (1)
9(139/73)+5y=2
1251/73+5y=2
5y=2-1251/73
Taking LCM on Right hand side
5y=(146-1251)/73
y=-1105/73*5
Y=-1105/73*5
y=-221/73

 x=139/73, y=-221/73

Check:
Put the values of x and y in equation (1)
9x+5y=2
9(139/73)+5(-221/73)=2
1251/73-1105/73=2
Multiply by 73 both sides
1251-1105=2*73
146=146

Now 

Put the values of x and y in equation (2)
-11x+2y=-27
-11(139/73)+2(-221/73)=-27
-1529/73-442/73=-27
Multiply by 73 both sides
-1529-442=-27*73
-1971=-1971