SOLUTION: Solve each of the following systems by the elimination method 1/4x - 1/6y = -2 -1/6x + 1/5y = 4

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve each of the following systems by the elimination method 1/4x - 1/6y = -2 -1/6x + 1/5y = 4       Log On


   

Question 154804: Solve each of the following systems by the elimination method
1/4x - 1/6y = -2
-1/6x + 1/5y = 4
Answer by orca(409) About Me  (Show Source):
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%281%2F4%29x-%281%2F6%29y=-2 ..............(1)
%28-1%2F6%29x%2B%281%2F5%29y=4 ..............(2)
Multiplying equation (1) by 12,equation (2) by 30 to clear fractions, we have
3x-2y=-24 .....................(3)
-5x%2B6y=120 ....................(4)
Multiplying equation (3) by 3, the systems becomes:
9x-6y=-72 .....................(5)
-5x%2B6y=120 ....................(6)
Adding equations(5) and (6)together, we have
9x-6y%2B%28-5x%2B6y%29=-72%2B120
Simplifying, we have
9x-6y-5x%2B6y=48
4x=48
x=12
Substituting x = 12 into equation(3), we obtain:
3%2A12-2y=-24
Solving for y, we have
36-2y=-24
36%2B24=2y
60=2y
30=y
So
y=30
Thus the solution is:
x = 12
y = 30