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To ease the solution to the system of equations, we convert all coefficients of x and y to whole numbers by multiplying each term of the equation by the gcd of the denominators.
Hence 3x + 1/4y=-3/4 multiplied by 4 becomes 12x + y = -3 (equation 1)
and -1/2x + 1/3y=8 multiplied by 6 becomes -3x + 2y = 48 (equation 2)
We shall solve by substitution.
the value of y in equation 1 is y= -3-12x
substituting this value into equation 2 gives
-3x + 2(-3-12x)=48
-3x - 24x=48+6
-27x = 54
to solve for y we substitute x= -2 into one of the equations say equation 1
12(-2) + y = -3
-24+ y = -3
y = 21
therefore x= -2 and y = 21
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