Question

Solve the following systems of equations:
99x + 101y = 499
101x + 99y = 501

Answer 1

The given equations are:
99x + 101y = 499.........(i)

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

Adding equation(i) and (ii), we get
$99x+101y+101x+99y=499+501$
$\Rightarrow 200x+200y=1000$
$\therefore x+y=5$........(iii)
Subtract equation equation(i) from equation(ii), we get
$\Rightarrow 101x-99x+99y-101y=501-499$
$\Rightarrow 2x-2y=2$
$\therefore x-y=1$......(iv)
Adding equation (iii) and (iv), we get
$2x=6$
$\therefore x=3$
Substitute $x=3$ in equation (iii), we get
$\Rightarrow 3+y=5\Rightarrow y=5-3\therefore y=2$

Hence the value of x=3 and y=2.