Question

99x+101y= 499, 101x+99y=501.find x​

Answer 1

• x=3
• y=2

The given system of equations are :

• 99x+101y=499 ====> (1)
• 101x+99y=501 ====> (2)

Adding equations (1) and (2), we get :

$\implies{99x+101x+101y+99y=499+501}$

$\implies{200x+200y=1000}$

$\implies{200(x+y)=1000}$

$\implies{(x+y)=1000/200=5}$

$\implies{(x+y) = 5 ====>(3)}$

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

$\implies{101x-99x+99y-101y=501-499}$

$\implies{2x-2y=2}$

$\implies{2(x-y)=2}$

$\implies{(x-y)=2/2=1}$

$\implies{(x-y) = 1 ====>(4)}$

Adding equation (iii) and equation (iv), we get :

$\implies{2x=5+1}$

$\implies{2x=6}$

$\implies{x=6/2}$

$\implies{x=3}$

Putting x = 3 in equation (3),we get :

$\implies{3+y=5}$

$\implies{y=5-3}$

$\implies{y=2}$

Hence, solution of given system of equation is :

• x=3
• y=2

Answer 2

x=3

y=2

hope it helps you.