Solve the following system of equations:

$99x+101y=499$$101x+99y=501$

Given:

The given system of equations is:

$99x+101y=499$

$101x+99y=501$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$99x+101y=499$......(i)

$101x+99y=501$.....(ii)

Adding equations (i) and (ii), we get,

$99x+101y+101x+99y=499+501$

$200x+200y=1000$

$200(x+y)=200\times5$

$x+y=5$.....(iii)

Subtracting equation (ii) from equation (i), we get, 

$99x+101y-(101x+99y)=499-501$

$-2x+2y=-2$

$-2(x-y)=-2$

$x-y=1$.....(iv)

Adding equations (iii) and (iv), we get,

$x+y+x-y=5+1$

$2x=6$

$x=\frac{6}{2}$

$x=3$

Using $x=3$ in equation (iii), we get,

$3+y=5$

$y=5-3$

$y=2$

Therefore, the solution of the given system of equations is $x=3$ and $y=2$.   

Tutorialspoint

Updated on: 10-Oct-2022

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