Please refer to Assignments Class 10 Mathematics Linear Equations Chapter 3 with solved questions and answers. We have provided Class 10 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 3 Linear Equations Class 10 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.
Linear Equations Assignments Class 10 Mathematics
VERY SHORT ANSWER TYPE QUESTIONS
Question. If x = 3m –1 and y = 4 is a solution of the equation x + y = 6, then find the value of m.
Ans. m = 1
Question. If ax + by = c and lx + my = n has unique solution then the relation between the coefficient will be:
(a) am ≠ lb
(b) am = lb
(c) ab = lm
(d) ab ≠ lm
Ans. (a) am ≠ lb
Question. If x = a and y = b is the solution of the equation x – y = 2 and x + y = 4, then the values of a and b are respectively _______ .
Ans. a = 3 and b = 1
Question. In ΔABC, √C = 3√B, √C = 2(√A + √B) then, √A, √B, √C are respectively.
(a) 30°, 60°, 90°
(b) 20°, 40°, 120°
(c) 45°, 45°, 90°
(d) 110°, 40°, 50°
Ans. (b) 20°, 40°, 120°
Question. If we draw lines of x = 2 and y = 3 what kind of lines do we get?
Ans. Intersecting lines
Question. What is the point of intersection of the line represented by 3x – 2y = 6 and the y-axis?
Ans. (0, –3)
Question. For 2x + 3y = 4, y can be written in terms of x as _______ .
Ans. y = (4-2x)/3
Question. Find the value of k for which pair of linear equations 3x + 2y = –5 and x – ky = 2 has a unique solution.
Ans. k ≠ -2/3
Question. Check whether the graph of the pair of linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 is intersecting lines or parallel lines.
Ans. Parallel lines
Question. The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solutions is ____ .
SHORT ANSWER TYPE (I) QUESTIONS
Question. Solve for x and y
x-y/2=3 and x/2 – 2y/3 = 2/3
Ans. 4, 2
Question. For what value of k, the following system of equations will be inconsistent
kx + 3y = k – 3
12x + ky = k
Ans. k = – 6
Question. For what value of p the pair of linear equations (p + 2)x – (2p + 1)y = 3(2p – 1) and 2x – 3y = 7 has a unique solution.
Ans. p ≠ 4
Question. Given the linear equation 2x + 3y – 12 = 0, write another linear equation in these variables, such that. geometrical representation of the pair so formed is (i) Parallel Lines (ii) Coincident Lines
Ans. (i) 4x + 6y + 10 = 0
(ii) 4x + 6y – 24 = 0
Question. Ram is walking along the line joining (1, 4) and (0, 6)
Rahim is walking along the line Joining (3, 4) and (1, 0)
Represent on graph and find the point where both of them cross each other
Ans. (2, 2)
SHORT ANSWERS TYPE (II) QUESTIONS
Question. Solve graphically the pair of linear equations 5x – y = 5 and 3x – 2y = – 4 Also find the co-ordinates of the points where these lines intersect y-axis
Ans. (2, 5) (0, – 5) and (0, 2)
Question. Solve by Cross – multiplication method
x/y + y/a a + b
x/a2 + y/b2 = 2
Ans. x = a2, y = b2
Question. Father’s age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of the father.
Ans. 45 years
Question. Solve the pair of linear equations
152x – 378y = – 74
– 378x + 152y = – 604
Ans. 2, 1
Question. On selling a T.V. at 5% gain and a fridge at 10% gain, a shopkeeper gain `₹ 2000. But if he sells the T.V. at 10% gain and fridge at 5% loss, he gains `₹ 1500 on the transaction. Find the actual price of the T.V. and the fridge
Ans. T.V. = ₹ 20,000 Fridge = ₹ 10,000
LONG ANSWER TYPE QUESTIONS
Question. Solve graphically the pair of linear equations 3x – 4y + 3 = 0 and 3x + 4y – 21 = 0
Find the co-ordinates of vertices of triangular region formed by these lines and x-axis. Also calculate the area of this triangle.
Ans. Solution (3, 3), Vertices (– 1, 0) (7, 0) and (3, 3), Area = 12 square units
Question. A two-digit number is 3 more than 4 times the sum of the digits. If 18 is added to the number, digits reversed. Find the number.
Question. A and B are two points 150 km apart on a highway. Two cars start with different speeds from A and B at same time. If they move in same direction, they meet in 15 hours. If they move in opposite direction, they meet in one hour. Find their speeds
Ans. 80 km/hr , 70 km/hr
Question. 8 Women and 12 men can complete a work in 10 days while 6 women and 8 men can complete the same work in 14 days. Find the time taken by one woman alone and that one man alone to finish the work.
Ans. 1 woman in 140 days, 1 man in 280 days
Question. Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the x-axis.
Ans. Area of quadrilateral ABCD where,
A(3, 0), B(5, 0)
C(5, 6), D(3, 2)
=1/2 × AB × (AD+BC)
= 1/2 × 2 × (6+2) = 8 sq. units.
Question. Solve for x and y
1/(2(2x+3y)) + 12/(7(3x – 2y)) = 1/2
For 2x + 3y ≠ 0
3x – 2y ≠ 0.
Ans. (2, 1)
Question. A railway half ticket cost half the full fare but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket costs ₹ 2530. One reserved first class ticket and one reserved first class half ticket from stations A to B costs ₹ 3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.
Ans. Let the cost of full and half ticket be ₹ x & ₹ x/2 and reservation charge by ₹ y per ticket.
Case I : x + y = 2530
Case 2 : x + y + x/2 + y = 3810
x = 2500, y = 3810
Full first class fare is ₹ 2500 and reservation charge is ₹ 30.
Question. In a two digit number, the ten’s place digit is 3 times the unit’s place digit. When the number is decreased by 54, digits get reversed. Find the original number.
Question. The ratio of incomes of two persons A and B is 3 : 4 and the ratio of their expenditures is 5 : 7. If their savings are ₹ 15,000 annually find their annual incomes.
Ans. ₹ 90,000, ₹ 1,20,000