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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-6-24x=48

-3x - 24x=48+6

-27x = 54

x= 54/-27

x= -2

to solve for y we substitute x= -2 into one of the equations say equation 1

12(-2) + y = -3

-24+ y = -3

y=24-3

y = 21

therefore x= -2 and y = 21

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