MATHEMATICS
PAIR OF LINEAR EQUATIONS
REVISION 1 MAX MARKS = 80
I. VERY SHORT ANSWERS (Answer any 5) ( 5 X 2 = 10)
1. Find the nature of the solution for the pair of linear equations
x + 2y + 5 = 0; -3x = 6y -1.
2. Find the value of k for which the pair of linear equations
5x + 2y – 7 = 0 and 2x + ky + 1 = 0 has no solution.
3. Check whether the point (-4,3) lies on both the lines represented by the linear equations x + y + 1 = 0
and x – y = 1.
4. Find the value of k for which x – y = 1, x + ky = 5 has a unique solution x = 2 and y = 1.
5. For which value of k , will the following pair of linear equations have no solution,
3x + y = 1 and (2k – 1)x + (k-1)y = 2k + 1.
6. Find the nature of the lines represented by pair of linear equations
3x + 2y = 7 and 4x + 8y -11 = 0.
7. If 17x – 19y = 53 and 19x -17y =55, then find the value of (x + y).
II SHORT ANSWER (Answer any 10 ) ( 10 X 3 = 30)
8. Solve for x and y:
a. x + 2y = 9 and y – 2x = 2.
9. Solve for x and y;
a. 7x – 2y = 5 and 8x + 7y = 15.
10. Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as
Nazma. How old are Rashmi and Nazma.
11. Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller
number is 13. Find the numbers.
12. If 2x + y = 13 and 4x – y = 17, find the value of (x – y).
13. A father is three times as old as his son. In 12 years, he will be twice as old as hi son. Find the sum of
the present ages of the father and his son.
14. The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2,
the fraction reduces to 1/3. Find the fraction.
15. Solve for x and y:
3x – 5y = 4, 2y + 7 = 9x.
16. Find the relation between p and q if x = 3 and y = 1 is the solution of the pair of equations x – 4y + p
= 0 and 2x + y – q – 2 = 0.
17. Find out whether the following pair of linear equations intersect at a point, parallel or coincident:
a. 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0
b. 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0
c. 6x – 3y + 10 = 0 and 2x – y + 9 = 0
18. Which of the following pairs of linear equations are consistent/inconsistent?
a. x + y = 5, 2x + 2y = 10
b. x – y = 8, 3x – 3y = 16
c. 2x + y – 6 = 0, 4x – 2y – 4 = 0
1
19. Half the perimeter of the rectangular garden, whose length is 4 m more than its width, is 36 m. find the
dimensions of the garden.
III LONG ANSWER ( 5 x 2 = 10)
20. Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per
student and Cricket ₹ y per student. School 'P' decided to award a total of ₹9,500 for the two games to
5 and 4 students respectively; while school ' Q ' decided to award ₹ 7,370 for the two games to 4 and
3 students respectively.
Based on the above information, answer the following questions:
(i) Represent the following information algebraically (in terms of x and y ).
(ii) What is the prize amount for hockey?
(iii)Prize amount on which game is more and by how much?
(iv) What will be the total prize amount if there are 2 students each from two games.
21. A book store shopkeeper gives books on rent for reading. He has variety of books in his store related
to fiction, stories and quizzes etc. He takes a fixed charge for the first two days and an additional charge
for subsequent day. Amruta paid Rs 22 for a book and kept for 6 days; while Radhika paid Rs 16 for
keeping the book for 4 days.
Assume that the fixed charge be Rs x and additional charge (per day) be Rs y.
1. The situation of amount paid by Radhika, is algebraically represented by
(a) x - 4y = 16 (b) x + 4y = 16 (c) x - 2y = 16 (d) x + 2y = 16
2. The situation of amount paid by Amruta, is algebraically represented by
(a) x - 2y = 11 (b) x - 2y = 22 (c) x + 4y = 22 (d) x - 4y = 11
3. What are the fixed charges for a book ?
(a) Rs 9 (b) Rs 10 (c) Rs 13 (d) Rs 15
4. What are the additional charges for each subsequent day for a book ?
(a) Rs 6 (b) Rs 5 (c) Rs 4 (d) Rs 3
5. What is the total amount paid by both, if both of them have kept the book for 2 more days ?
(a) Rs 35 (b) Rs 52 (c) Rs 50 (d) Rs 58
IV ASSIGNMENT QUESTIONS : (3 x 10 = 30)
22. Draw the graph of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the
vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
23. Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are
given by 2y – x = 8, 5y – x = 14 and y – 2x = 1.
24. Solve the pair of linear equations by elimination method, substitution method and by graphical method:
𝑥 2𝑦 𝑦
+ = −1. 𝑎𝑛𝑑 𝑥 − =3
2 3 3
