SSC (Marathi Semi-English) 10thMaharashtra State Board
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Solve the following simultaneous equations: 7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33 - SSC (Marathi Semi-English) 10th - Algebra

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Question

Solve the following simultaneous equations: `7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33`

 

 

Solution

`7/(2x+1)+13/(y+2)=27`                             .........(1)

`13/(2x+1)+7/(y+2)=33`                           ...........(2)

Substituting`1/(2x+1)=m` and`1/(y+2)=n` in equations (1) and (2), we get

7m+13n=27    .............(3)

and13m+7n=33  ..........(4)

Adding equations (3) and (4), we get

20m+20n=60

∴m+n=3      ...............(5)

Subtracting equation (3) from equation (4), we get

6m-6n=6

∴m-n= 1        ...........(6)

Adding equations (5) and (6), we get

2m= 4

∴ m= 2

Substituting m = 2 in equation (5), we get

2+n= 3

∴n= 1

Resubstituting the values of m and n, we get

`1/(2x+1)= 2 and 1/(y+2)=1`

∴4x+2= 1  and  y+2= 1

∴4x= -1  and  y=1-2

∴x=`-1/4`  and y= -1

 
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Solution Solve the following simultaneous equations: 7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33 Concept: Equations Reducible to a Pair of Linear Equations in Two Variables.
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