1. Construction of linear equations

2. Linear Equation
An linear equation is an algebraic expression that is always equated to either a numerical value or another algebraic expression. For example: 7x + 3 = 10
LHS
RHS
The equality sign (=) shows that the value of the
expression to the left of the ‘=’ sign is equal to the value
of the expression to the right of the ‘=’ sign.
LHS = RHS

3. Some more examples of linear equation 4a + 1 = 8 7p – q = 18 5y + 3 = 2y + 7 3m + n = 5m – n

4. Equation and Solution
Consider the expression 7x + 3, where x is the variable. When x = 2, the value of the expression is 7x + 3 =(7 * 2) + 3 = = 17. This can be written as 7x + 3 = 17, when x = 2. 7x + 3 = 17 is called an equation. x = 2 is called the solution.
Replacing x with 2

5. How to construct a linear equation?
This is Sita. Sita goes
to a fruit shop to buy
apples and oranges.
She has Rs.120 with
her.
She returns home
with 4 apples and 2
oranges.
At the shop, the price of
the fruits are not given.
She asks the shopkeeper
to give apples and
oranges for Rs.120
Cost of 1 apple = x
Cost of 1 orange = y
Sita bought 4 apples and 2 oranges.

6. Cost of 4 apples and 2 oranges is 120
Cost of 1 apple  x
Cost of 1 orange  y
Cost of 4 apples and 2 oranges is 120
4 * cost of 1 apple * cost of 1 orange = 120
4x y = 120
Therefore, 4x + 2y = 120

7. Cost of 10 chairs and 4 tables is 4000
Example 1: The price of 10 chairs and 4 tables is Construct a linear equation. Solution:
Cost of 1 chair  x
Cost of 1 table  y
Cost of 10 chairs and 4 tables is 4000
10 * cost of 1 chair * cost of 1 table = 4000
10x y = 4000
Therefore, 10x + 4y = 4000
Ans: 10x+4y = 4000

8. Example 2: A rectangle of some dimensions has perimeter 50 mts.
Construct a linear equation.
Solution:
Length of the rectangle  l mts
Breadth of the rectangle  b mts
Perimeter of the rectangle = l + l + b + b
l + l + b + b = 50 mts
grouping like terms
2l + 2b = 50 mts
taking 2 common
2 (l + b) = 50 mts
Ans: 2 (l + b) = 50
l mts
b mts

9. Example 3: One third of a number plus 6 is 10
Example 3: One third of a number plus 6 is 10. Construct a linear equation Solution: One third of a number plus 6 is 10 * number + 6 = 10 * n + 6 = 10 n + 6 = 10 Ans: n + 6 = 10

10. Try These Construct linear equations for the following:
The sum of five times of x and 3 is 28.
The cost of 6 pens and 5 pencils is 80 rupees