Model Problems
Chapter Name: Pair of Linear Equations in two Variables
1. Cost of 5 pens and 6 notebooks is Rs. 200. Express the given data in the form of linear equation in two variables.
2. Sum of two numbers is 23. Express the given data in the form of linear equation in two variables.
3. In a mathematics test, Ramu got 2 marks more than 3 times of marks of Raju. Express the given data in the form of linear equation in two variables.
4. Cost of a pen is 1 rupee more than twice of cost of pencil. Express the given data in the form of linear equation in two variables.
5. Solve 2x + 3y - 6 = 20 and x + 2y = 2 by Elimination method.
6. Solve 3x + y = 2 and 2x + y = 3 by Elimination method.
7. Solve x + y = 4 and x + 3y = 10 by Substitution method.
8. Solve 2x - y = 10 and 3x - 2y = 14 by Substitution method.
9. Check whether 5x + 2y = 8 and 2x - y = 4 are consistent or inconsistent?
10. Lakshmi said that "x - 2y - 6 = 0 and 3x - 6y - 18 = 0 have infinity many solutions". Do you agree with her? Justify.
11. Surya said that "3x + y = 10 and 6x + 2 y - 5 = 0 are represent parallel lines." Do you agree? Justify your answer.
12. Check whether x - y = 3 and 3x - 3y = 4 are intersecting lines or parallel lines?
13. If "2x - 3py = 7 and 3x - 9y = 10" are represent a railway track, then find the value of 'p'.
14. For what value of 'k', "3x + 2y = 1 and 2kx + 4y = 2 having No solution".
15. If "x - 2y = 4 and 3x - 6y = 5 are inconsistent", then find the value of 'm'.
16. For which value of 'n', "x + 2y = 4 and 3x + ny = 10 have only one solution".
17. Solve: 3x + 4y = 13 and 2x - 3y = 3 graphically.
18. Find the solution of 2x + y = 7 and x + 3y = 6 by graphical representation.
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