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Question

Solve the following pair of linear equations:
2x+3y=2
4x9y=1
(Where x>0,y>0)

A
x=9,y=4
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B
x=4,y=9
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C
x=3,y=2
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D
x=12,y=13
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Solution

The correct option is B x=4,y=9
Given,
2x+3y=2
4x9y=1
(Where x>0,y>0)

The pair of equations are not linear. We will substitute
1x as u2 and 1y as v2 (As x>0,y>0)
Then we will get the equations as
2u+3v=2.........(i)
4u9v=1.........(ii)

We will use method of elimination to solve the equation
Multiply equation (i) by 3
6u+9v=6.........(iii)

Adding (ii) and (iii) we get
10u=5
u=12
Substituting u in (i), we get
2(12)+3v=2
3v=1
v=13
So x=1u2=4
y=1v2=9

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