CBSE Class 10 Maths Linear Equations

Linear Equations in two variables in two

variables

Linear equation in two variables can be written as :-

ax+by+c=0       and a, b and c are real numbers.

This equation has infinitely many solution. When we consider two linear equation together then we say it a system of two variable x and y. such as.

5x + 3y + 2 = 0

2x - 3y + 5 = 0

Algebraic solution of system of linear equation:

1. Elimination by substitution:

Let us consider a system of linar equations: 

From equation (1) we get

x = (1 + 7y)/2

Putting the value of x in e.q. (2) we get

Or, 2 + 14y + 3y = 15

Or, 17y = 13

Or, y = 13/17

Putting value of y in eq (1) we get

Or, 2x = 1 + 91/17

Or, 2x = (17+91)/17

Or, x = 108/34

Or, x = 54/17

x=54/17, y=13/17

Exercise

1. If twice the son’s age in years is added to the age of his father the sum is 90. If twice the father’s age in year is added to the age of the son, the sun in 120. Find their ages.

2. Ram is three times as old as Rahim. Five years later, Ram will be two-and-a –half times as old as Rahim. How old are Ram and Rahim now?

3. If the numerator of a fraction is multiplied by 2 and its denominator is increased by 2, it becomes 6/7. If instead we multiply the denominator by 2 and increase the numerator by 2 it reduces to 1/2. What is the fraction?

4. A fraction becomes 4/5 if 1 is added to each of the numerator and the denominator. However, if we subtract 5 from each, the fraction becomes 1/2 find the fraction.

5. If we add 1 in the numerator of a fraction and subtract 1 from its denominator, the fraction becomes 1, It is also given that the fraction becomes 1/2 when we add 1 to its denominator, and then what is the fraction.

6. If we add 5 to the denominator and subtract 5 from the numerator of fraction, it reduces to 1/7 if we subtract 3 from the numerator and add 3 to its denominator it reduces to 1/3. Find the fraction.

7. The denominator of a fraction is 4 more than twice the numerator. When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.

8. The sum of the numerator and denominator of a fraction is 4 more than twice the numerator if the numerator and denominator are increased by 3, they are is the ratio 2 : 3. Determine the fraction.

9. Two audio cassettes and three video cassettes cost Rs. 340. but three audio cassettes and two video cassettes cost Rs 260. Find the price of an audio cassettes and that of a video cassettes.

10. Mala purchased 5 chairs and 2 tables for Rs. 1625. Reshma purchased 2 chairs and 1 table for Rs. 750. Find the cost per chair and per table.

Please refer to attached file for CBSE Class 10 Maths Linear Equations