Answer:
x = 1; y = 5/4
Explanation:
7/x - 5/y = 3
2/x + 25/(2y) = 12
The LCD of first equation is xy. Multiply both sides of the first equation by xy.
xy(7/x) - xy(5/y) = 3xy
7y - 5x = 3xy
The LCD of second equation is 2xy. Multiply both sides of the second equation by 2xy.
2xy(2/x) + 2xy(25/2y) = 24xy
4y + 25x = 24xy
7y - 5x = 3xy
4y + 25x = 24xy
Multiply the top equation by -8 and add to bottom equation.
-56y + 40x = -24xy
(+) 4y + 25x = 24xy
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-52y + 65x = 0
65x = 52y
x = 52y/65
7y - 5x = 3xy
7y - 5(52y/65) = 3(52y/65)y
455y - 260y = 156y²
156y² - 195y = 0
4y² - 5y = 0
y(4y - 5) = 0
y = 0 or 4y = 5
y = 0 or y = 5/4
7/x - 5/y = 3
y cannot equal zero.
7/x - 5/y = 3
7/x - 5/(5/4) = 3
7/x - 4 = 3
7/x = 7
x = 1
Solution: x = 1; y = 5/4