Question 154804
{{{(1/4)x-(1/6)y=-2}}} ..............(1)
{{{(-1/6)x+(1/5)y=4}}} ..............(2)
Multiplying equation (1) by 12,equation (2) by 30 to clear fractions, we have

{{{3x-2y=-24}}} .....................(3)
{{{-5x+6y=120}}} ....................(4)
Multiplying equation (3) by 3, the systems becomes:
{{{9x-6y=-72}}} .....................(5)
{{{-5x+6y=120}}} ....................(6)
Adding equations(5) and (6)together, we have
{{{9x-6y+(-5x+6y)=-72+120}}}
Simplifying, we have
{{{9x-6y-5x+6y=48}}}
{{{4x=48}}}
{{{x=12}}}
Substituting x = 12 into equation(3), we obtain:
{{{3*12-2y=-24}}}
Solving for y, we have
{{{36-2y=-24}}}
{{{36+24=2y}}}
{{{60=2y}}}
{{{30=y}}}
So
{{{y=30}}}
Thus the solution is:
x = 12
y = 30