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44 votes
Solve simultaneously please

Solve simultaneously please-example-1
User Wikk
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1 Answer

15 votes
15 votes

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

---------------------------------

-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

User Campino
by
2.9k points