Question

The solution of eqution of equations $x+y=10,2x+y=18$, and $4x-3y=26$, will be

• A. Only one solution
• B. No solution
• C. Infinite solution
• D. None of these

Answer 1

Answer: (A)

$x+y=10$
$2x+y=18$
and $4x-3y=26$
are equations of three lines respectively
Solving of equation (i) and (ii), we get $x=8$ and $y=2$
Put the values of $x$ and $y$ in equation (iii),
L. H.S $=4x-3y=4\times 8-3\times 2=32-6=26=$ R.H.S.
$\therefore$ Point $(8,2)$ lies on line $4x-3y=26$, so these three lines are concurrent. Hence, these three equations have one and only one solution