**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:**

Solution: **(i) intersecting lines **

2x + 3y – 8 = 0

The condition for intersecting lines is

So we multiply any value with a1 and not with b1

If we multiply by 2 second such equation will

**4x + 3y – 8 = 0**

**(ii)parallel lines** the condition for parallel lines is

So multiply with a_{1} , b_{1} with any number and not multiply with c

if we multiply by 2 then second equation will

**4x + 6y – 8 = 0**

**(iii) coincident lines ** the condition for coincident lines are

So multiply by any number with whole equation

If we multiply by 2 we get

**4x + 6y – 16 = 0 **