Linear Equations In Two Variables

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LINEAR EQUATIONS IN TWO VARIABLES Practice Exercise - 1 ___________________________________________________________________________________

Q-1.State which of the following equations are linear equations in two variables and express them in the standard form (1) 2x = 6 (5) xy = 7

(2) 2x + 5y =3 (6) x2y = 8

(3) 5x2 = 6y (4) x2 + 2x + 3 = 0 (7) 4x + 5y = 3 (8) 3y = 2

Q-2.Find three elements of the solution sets of the following equations. (1) 2x = 6 (2) 2x + 5y =3 (5) x + y = 7 (6) 2x + 4y = 8

(3) 5x - 6y = 4 (4) 4x + 3y = 0 (7) 4x + 5y=3 (8) 3y = 2

Q-3.Draw the graph of the following linear equations in two variables. (1) 2x = 6 (2) 2x - 3y =0 (5) x + y = 7 (6) 2x + 4y = 8 (9) x – y -7 = 0 (10) 2x - 6y =12

(3) 5x- 10y= 15 (7) 4x + 4y =12 (11) 4x + 4y =12

(4) 4x + 3y = 0 (8) 3y = 6 (12) 5x - 2y -8 = 0

Q-4.Solve the following equations using the graphical method of solution (1) (2) (3) (4) (5) (6)

x + 2y =3 2x + y = 5 3x + 2y = 9 x + 4y –2 = 0 4x – 3y – 2 = 0

& & & &

2x + y =3 y=3 x + 4y – 8 =0 & 2x – y = -5 5x – y -8 =0

Q-5.The sum of the ages of John, Jenny, Marc is x years. After 3 years what will be the sum of their ages. Q-6.What is the nature of the graph of the equation y = 5? Q-7.If the sum of the two numbers is 250 and their difference is 50, then what is the larger number? Q-8.What is the nature of the graph of the equation 3x = 6? Q-9.The sum of the ages of Mary, Aniston, Sheryl is x years. Before 3 years what was the sum of their ages?

Q-10.Solve the following problems (1) In a two digit number, the ten’s digit is twice the units digit. If we reverse the order of digits, then the difference of the original and the new number is 27. Find the new number. (2) The length of the room is 4 times its breadth. If the perimeter of the room is 100 cm. Find the length of the room. (3) The sum of the digits of the two digit number is 9. If the digits are reversed and the new number is subtracted from the original number we get 27. Find the original number. (4) Two years ago a man was 6 times as old as his son. 18 years hence he will be twice as old as his son. What are the present ages of man and his son? (5) (6) The difference between two numbers is 9 and the difference between their squares is 207. What are the numbers? (7) Two numbers are in ration 3 : 5. If each is increased by 10 the ratio becomes 5 : 7. Find both the numbers. (8) Manoj goes to college on a motorcycle with the speed of 80 km / hour. Exactly at half way, she takes a rickshaw which travels at the speed of 40 km /hour. If the total time taken is 30 minutes, then find the time taken in both the travels, i.e. on a motorcycle and rickshaw. (9) Pinky deposited certain amounts at the rates 5 and 5.5%. She