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in Linear Equations by (53.1k points)

The values of x and y satisfying (x + 3) (y – 5) = xy + 39 and (x – 2) (y + 3) = xy – 40 respectively are : 

(a) 6 and 8 

(b) 6 and –8 

(c) –6 and 8 

(d) –6 and –8

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1 Answer

+1 vote
by (49.2k points)

(c) –6 and 8

(x + 3)(y – 5) = xy + 39

\(\Rightarrow\) xy + 3y – 5x – 15 = xy + 39

\(\Rightarrow\) –5x + 3y = 54  5x – 3y = –54 ..........(i)

(x – 2) (y + 3) = xy – 40

\(\Rightarrow\) xy – 2y + 3x – 6 = xy – 40

\(\Rightarrow\) –2y + 3x = –34 \(\Rightarrow\) 3x – 2y = – 34 .............(ii)

Multiply (i) by 3 and (ii) by 5 and then subtract eqn (ii) from eqn (i). 

so that we get solution.

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