Step-2 : Increase (or decrease) the quantities in proportion to make one of the quantities equal in
both situations. Here, we make the number of pens equal.
In Step 2, we observe a simple proportional reasoning.
Since Siri bought 3 books and 2 pens for `80,so for 9 books and 6 pens:
3 × 3 = 9 books and 3 × 2 = 6 pens, the cost will be 3 × 80 = `240 (1)
Similarly, Laxmi bought 4 books and 3 pens for `110, so:
After comparing (1) and (2), we can easily observe that 1 extra book costs
`240 - ` 220 = `20. So one book cost is `20.
Siri bought 3 books and 2 pens for `80. Since each book costs `20, 3 books cost ` 60.
So the cost of 2 pens become ` 80 - ` 60 = ` 20.
So, cost of each pen is `20 ÷ 2 = `10.
Let us try these costs in Laxmi's situation. 4 books will cost ` 80 and three pens will cost
` 30 for a total of ` 110, which is true.
From the above discussion and calculation, it is clear that to get exactly one solution (unique
solution) we need at least two independent linear equations in the same two variables.
In general, an equation of the form ax + by + c = 0, where a, b, c are real numbers and
where at least one of a or b is not zero i.e. 2 2 a b + ¹ 0 , is called a linear equation in two
variables x and y.
TRY THIS
Mark the correct option in the following questions:
1. Which of the following equations is not a linear equation?