Construction of linear equations

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

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

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 = 14 + 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

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.

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 + 2 * cost of 1 orange = 120 4x + 2y = 120 Therefore, 4x + 2y = 120

Cost of 10 chairs and 4 tables is 4000 Example 1: The price of 10 chairs and 4 tables is 4000. 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 + 4 * cost of 1 table = 4000 10x + 4y = 4000 Therefore, 10x + 4y = 4000 Ans: 10x+4y = 4000

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

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

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