[CBSE 2025] Solve the following system of equations algebraically . . .

Question : Solve the following system of equations algebraically :

37x+63y=137

63x+37y=163

CBSE 2025

Solution : 

 

37x+63y=137 — (1) 

63x+37y=163 — (2) 

Adding equation (1) and (2) 

37x+63y=137

63x+37y=163
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100x+100y=300

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100(x+y)=300
x+y=300/100

x+y=3 — (3)

Subtracting equation (2) from (1) 

37x+63y=137

63x+37y=163
-     -         - 
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-26x+26y=-26

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26(-x+y)=-26
-x+y=-26/26
-x+y=-1 — (4) 

Now Solving equation (3) and (4) by elimination method

 x+y=3

-x+y=-1
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0 +2y=2

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2y=2

y=2/2

y=1

Putting in equation (3)
x+1=3
x=3-1
x=2

Hence, x=2 and y=1

Similar Question : 

1.) Solve the following system of equations algebraically :

73x-37y=109

37x-73y=1

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x=2, y=1

2.) Solve the following pair of equations algebraically :

101x+102y=304

102x+101y=305

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x=2, y=1