# 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

(ii) parallel lines

(iii) coincident lines

**Solution:**

For any pair of linear equation

a_{1} x + b_{1} y + c_{1} = 0

a_{2} x + b_{2} y + c_{2} = 0

a) a_{1}/a_{2} ≠ b_{1}/b_{2} (Intersecting Lines)

b) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2} (Coincident Lines)

c) a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2} (Parallel Lines)

(i) intersecting lines

Condition: a_{1}/a_{2} ≠ b_{1}/b_{2}

2x + 3y - 8 = 0

a_{1}= 2

b_{1}= 3

So, considering a_{2}= 3 and b_{2} = 2 will satisfy the condition for intersecting lines c_{2} can be any value.

a_{1}/a_{2}= 2/3

b_{1}/b_{2}= 3/2

2/3 ≠ 3/2

∴ Another linear equation is 3*x *+ 2 *y *- 6 = 0

(ii) parallel lines

Condition: a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

2x + 3y - 8 = 0

a_{1}= 2

b_{1}= 3

c_{1}= - 8

So, considering a_{2} = 4, b_{2} = 6, c_{2} = 9 will satisfy the condition for parallel lines.

a_{1}/a_{2}= 2/4 = 1/2

b_{1}/b_{2}= 3/6 = 1/2

c_{1}/c_{2}= - 8/9

From above:

a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

Therefore, another linear equation is = 4*x *+ 6 *y *+ 9 = 0

(iii) coincident lines

Condition: a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

2x + 3y - 8 = 0

Condition: a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}

2x + 3y - 8 = 0

a_{1}= 2

b_{1}= 3

c_{1}= - 8

So, considering a_{2} = 4, b_{2} = 6, c_{2} = - 16 will satisfy the condition for parallel lines.

a_{1}/a_{2}= 2/4 = 1/2

b_{1}/b_{2}= 3/6 = 1/2

c_{1}/c_{2}= - 8/-16 = 1/2

From above:

a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

Therefore, linear equation is 4*x *+ 6 *y *-16 = 0

**Video Solution:**

## 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 (ii) parallel lines (iii) coincident lines

### NCERT Solutions for Class 10 Maths - Chapter 3 Exercise 3.2 Question 6:

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 (ii) parallel lines (iii) coincident lines

For the linear equation 2x + 3y - 8 = 0, then the other linear equation such that both equations become intersecting lines is 3x + 2y - 6 = 0 and for parallel lines is 4x + 6y + 9 = 0 and for the coincident lines 4x + 6y - 16 = 0