First slide

Equation of line in Straight lines

Question

Point of intersection of family of lines given by $(3 x + 4 y - 7) + λ (5 x - 2 y - 3) = 0$ is

Easy

A

$(1, 1)$
B

$(2, 2)$
C

$(3, 3)$
D

$(- 1, - 1)$

Solution

The point of intersection of family of lines given is same as the point of intersection of the lines $3 x + 4 y - 7 = 0, 5 x - 2 y - 3 = 0$
Eliminate y
$\begin{matrix} (3 x + 4 y - 7) + 2 (5 x - 2 y - 3) = 0 \\ 3 x + 4 y - 7 + 10 x - 4 y - 6 = 0 \\ 13 x - 13 = 0 \\ x = 1 \end{matrix}$

Substitute $x = 1$ in the equation $5 x - 2 y - 3 = 0$ to get the y coordinate
$\begin{matrix} 5 (1) - 2 y - 3 = 0 \\ - 2 y + 2 = 0 \\ y = 1 \end{matrix}$
Therefore, the point of intersection of family of lines is $(1, 1)$

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