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Elimination Method of Finding Solution of a Pair of Linear Equations

Solve for x a...

Question

Solve for x and y:

$3 (2 x + y) = 7 x y, 3 (x + 3 y) = 11 x y (x \neq 0 a n d y \neq 0) .$

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Solution

Given equation

3(2x+y)=7xy
3(x+3y)=11xy
where (x≠0 and y≠0).

6x+3y=7xy.......(1)
3x+9y=11xy .........(2)

multiply by 2 in eq (2)
⇒ 6x + 18 y = 22 xy.....(3)

Subtract eq (1) from eq (3) we get

15y = 15 xy

x = 1

Put the value of x in eq (1)

6x+3y=7xy
=6(1)+3y=7(1)y
=6=7y-3y
=6/4=y
y=3/2

So, x = 1 and y = 3/2 is the solution

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