Six persons initiated a campiagn against child labour. Each time they visit a new locality, two persons join them in the campaign from that locality. Taking x as the no. of localities and y as the total no. of persons, form a linear equation in two variables. How many localities have they visited when the total no. of persons is 16?
y = 2 x + 6
16 = 2 x + 6
10 = 2 x
x = 5
To form a linear equation in two variables, let's assign x as the number of localities and y as the total number of persons.
Given that each time they visit a new locality, two persons join the campaign from that locality, we can determine the equation.
Initially, there were six persons, so y = 6. For every locality they visit, two persons join, which can be represented as 2x. Therefore, the equation becomes:
y = 6 + 2x
Now, we want to find the number of localities (x) when the total number of persons (y) is 16.
Let's substitute y = 16 into the equation:
16 = 6 + 2x
To solve for x, we need to isolate it on one side of the equation. Let's start by subtracting 6 from both sides:
16 - 6 = 6 - 6 + 2x
10 = 2x
Now, divide both sides by 2 to solve for x:
10/2 = 2x/2
5 = x
So, they have visited 5 localities when the total number of persons is 16.