Given the linear equation $2x+3y-8=0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.

Given:

Given linear equations is $2x\ +\ 3y\ -\ 8\ =\ 0$.

To do:

We have to write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.

Solution:

Let another linear equation be $3x+2y-5=0$

Comparing the given pair of linear equations with the standard form of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$, we get,

$a_1=2, b_1=3$ and $c_1=-8$

$a_2=3, b_2=2$ and $c_2=-5$

Here,

$\frac{a_1}{a_2}=\frac{2}{3}$

$\frac{b_1}{b_2}=\frac{3}{2}$

$\frac{c_1}{c_2}=\frac{-8}{-5}=\frac{8}{5}$

$\frac{a_1}{a_2} ≠ \frac{b_1}{b_2}$

Therefore, the required line which intersects with the given line at one point is $3x+2y-5=0$.

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Updated on: 10-Oct-2022

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