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Solve 99x + 101y = 499

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Solve 99x + 101y = 499

Posted by Manjinder Singh Manjinder Singh 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given, 99x + 101y = 499 ....(i)
101x + 99y = 501... (ii)
Adding eqn. (i) and (ii),
( 99x + 101y ) + (101x + 99y ) = 499 + 501
99x + 101y + 101x + 99y = 1000
200x + 200y = 1000
x + y = 5 ...(iii)
Subtracting eqn. (ii) from eqn. (i), we get
( 99x + 101y ) - (101x + 99y ) = 499 - 501
99x + 101y - 101x - 99y = -2
-2x + 2y = - 2
or, x - y= 1 ........ (iv)
Adding equations (iii) and (iv)
x + y + x - y = 5 + 1
2x = 6
{tex}\therefore {/tex} x = 3
Substituting the value of x in eqn. (iii), we get
3 + y = 5
y = 2
Hence the value of x and y of given equation are 3 and 4 respectively.

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