Question

solveof the given system of equations....

Answer 1

$\binom{99x + 101y = 499}{101x + 99y = 501} \\ \\ solve \: for \: x \\ \\ \binom{99x + 101y = 499}{x = \frac{501}{101} - \frac{99}{101}y } \\ \\ substitute \: the \: given \: value \: in \: the \: equation \\ 99x + 101y = 499 \\ \\ 99( \frac{501}{101} - \frac{99}{101} y) + 101y = 499$


$now \: solve \: for \: y \\ \\ \frac{49599}{101} - \frac{9801}{101} y + 101y = 499 \\ \\ \frac{49599}{101} + \frac{400}{101} y = 499 \\ \\ mutiply \: both \: sides \: by \: 101 \\ \\ 49599 + 400y = 50399 \\ \\ 400y = 50399 - 49599 \\ \\ 400y = 800 \\ \\ y = \frac{800}{400} \\ \\ y = 2$


$substitute \: the \: value \: of \: y \: in \\ x = \frac{501}{101} - \frac{99}{101} y \\ \\ x = \frac{501}{101} - \frac{99}{101} \times 2 \\ \\ x = \frac{501}{101} - \frac{198}{101} \\ \\ x = 3$

Therefore the possible solution for the system of Equation is (x,y) = (3,2)

Answer 2

99x+101y=499. -(1)
101x+99y=501. -(2)
adding equation 1 and 2
99x+101y+101x+99y=499+501
200x+200y=1000
200(X+y)=1000
x+y =1000÷200
x+y=5. -(3)
subtracting 1 and 3
101x-99y+99y-101y=501-499
2x-2y=2
2(X+y)=2
x-y=2÷2
x-y =1. (4)
adding 4 and 3
2x=5+1
x=6÷2=3
putting X=3 in equation (3)
3+y=5
y=5-3=2
Hence, X=3,y=2

I hope this will help you