Question 511476
The original fraction is x/y.
.
We're told:
x-2 / y -2 = 1/2
so
2(x-2) = y-2
2x -4 = y -2
2x -2 = y
so
y = 2x -2
.
We're also told:
x+1 / y-2 = 3/4
so
4x+4 = 3y-6
3y = 4x + 10
y = 4/3x + 10/3
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Now we have two linear equations and two unknowns.
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We can graph them see where the intersect.
.
{{{graph(500,500,-5,15,-5,15,2*x-2,4/3*x+10/3)}}}
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Or we can solve the two equations.
.
y = 2x -2
3y = 4x + 10
.
3y = 6x -6
3y = 4x +10
0 = 2x -16
2x = 16
x = 8
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substitute
.
y = 2(8) -2
y = 14
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So it appears the first equation is
8/14
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But always check your answer
.
(x-2)/(y-2) = 6/12 = 1/2
(x+1)/(y-2) = 9/12 = 3/4
.
Answer:  x=8, y=14
.
Done.