Question

Find a fraction that reduces to 3/4 when both the numerator and denominator are decreased by i, and reduces to 4/5 when both the numerator and denominator are each increased by 1. I know the answer is 7/9, but i don't know how to solve (i must use a system of equations).

Answer 1

x-1/y-1=3/4 x+1/y+1=4/5 (cross multiplication)
(cross multiplication) 5x+5=4y+4------>5x-4y=-1
4x-1=3y-3---->4x-3y=1(eq.1)
5(4x-3y=1)---->20x-15y=5
4(5x-4y=-1)--->-20x+16y=4
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1y=9
y= 9/1=9 4x-3y=1(put 9)
4x-3(9)=1-->4x-27=1
4x=1+27
x=28/4-->7
x/y=7/9