Question 6 (i)
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:
(i) Intersecting lines

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Solution

Intersecting lines:
For this condition,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Hence, the second line can be;
2x + 4y - 6 = 0 as
$\frac{a_{1}}{a_{2}} = \frac{2}{2} = 1$
$\frac{b_{1}}{b_{2}} = \frac{3}{4}$ and
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

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Similar questions

Q. Given the linear equation

2 x + 3 y - 8 = 0

, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines.

Question 6 (iii)
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:
coincident lines

Q. Question 6 (ii)
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:
(ii) Parallel lines

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Question 6 (i) 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: (i) Intersecting lines

Intersecting lines: For this condition, a1a2≠b1b2 Hence, the second line can be; 2x + 4y - 6 = 0 as a1a2=22=1 b1b2=34 and a1a2≠b1b2

Question 6 (i)
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:
(i) Intersecting lines

Intersecting lines:
For this condition,
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Hence, the second line can be;
2x + 4y - 6 = 0 as
$\frac{a_{1}}{a_{2}} = \frac{2}{2} = 1$
$\frac{b_{1}}{b_{2}} = \frac{3}{4}$ and
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$