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in Linear Equations by (49.1k points)
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Solve:

\(\frac{x + 2}{y + 2} + 2 =0, \frac{x - 4}{y-2} =\frac{x -1}{y + 7}\)

(a) x = 2, y = 4

(b) x = –2, y = 4

(c) x = 2, y = –4

(d) x = –2, y = –4

1 Answer

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Best answer

Correct option is (c) x = 2, y = –4

Given,

\(\frac{x + 2}{y + 2} + 2 =0\)

⇒ \(\frac{x + 2y + 6}{y + 2} = 0\)

⇒ x + 2y + 6 = 0    .......(1)

\(\frac{x - 4}{y-2} =\frac{x -1}{y + 7}\)

⇒ xy + 7x − 4y − 28 = xy − 2x − y + 2

⇒ 9x − 3y = 30

⇒ 3x − y = 10

⇒ y = 3x − 10     .....(2)

Putting the value of y in eq(1), we get

x + 2(3x − 10) + 6 = 0

⇒ 7x = 14

⇒ x = 2

Putting the value of x in eq(2), we get

y = 6 − 10 = −4

So, we get the value of x = 2 and y = −4.

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