Question

Among the given options, the point of intersection of the lines $x-y-1=0$, $4x+3y-25=0$ and $2x-3y+1=0$ is

• A. $(4,1)$
• B. $(4,2)$
• C. $(4,3)$
• D. $(4,4)$

Answer 1

The correct option is C

$(4,3)$

We shall first find the point of intersection of the lines $x-y-1=0$ and $4x+3y-25=0$, as follows:

$4x+3y-25=0$ $----\left(1\right)$

$x-y-1=0$ $----\left(2\right)$

From $\left(1\right)$, $4x+3y=25$ $----\left(3\right)$

$\left(2\right)\times 3$ gives $3x-3y=3$ $-----\left(4\right)$

Adding $\left(3\right)$ and $\left(4\right)$, we get,

$7x=28$

$⟹x=4$

Hence $y=3$

$\therefore$ Point of intersection is $(4,3)$.

Putting this point in the L.H.S. of $2x-3y+1=0$, we get,

$2\left(4\right)-3\left(3\right)+1$

= $8-9+1$

=$0$

= R.H.S.

Hence $(4,3)$ is the right answer.

[An easy way out:

The given options may be substituted in the given equations. The point which satisfies all the three equations is the point of intersection of the three lines]