Worksheet: Pair of Linear Equations in Two Variables

# Pair of Linear Equations in Two Variables Class 10 Worksheet Maths Chapter 3

## Multiple Choice Questions

Q1: A pair of linear equations which have a unique solution x = 2, y = – 3 is:
(a) 2x – 3y = – 5, x + y = – 1
(b) 2x + 5y + 11 = 0, 4x + 10y + 22 = 0
(c) x – 4y – 14 = 0, 5x – y – 13 = 0
(d) 2x – y = 1, 3x + 2y = 0

Q2: If a system of a pair of linear equations in two unknowns is consistent, then the lines representing the system will be
(a) parallel
(b) always coincident
(c) always intersecting
(d) intersecting or coincident

Q3: The pair of equations x = 0 and y = 0 has
(a)
one solution
(b)
two solutions
(c)
infinitely many solutions
(d)
no solution

Q4: A pair of system of equations x = 2, y = -2; x = 3, y = – 3 when represented graphically enclose
(a) Square
(b) Trapezium
(c) Rectangle
(d) Triangle

Q5: If two lines are parallel to each other then the system of equations is
(a)
consistent
(b)
inconsistent
(c)
consistent dependent
(d)
(a) and (c) both

## Fill in the blanks

Q1: If in a system of equations corresponding to coefficients of member, equations are proportional then the system has ______________ solution (s).

Q2: A pair of linear equations is said to be inconsistent if its graph lines are ____________.
Q3:
A pair of linear equations is said to be ____________ if its graph lines intersect or coincide.
Q4:
A consistent system of equations where straight lines fall on each other is also called _____________ system of equations.
Q5: Solution of linear equations representing 2x – y = 0, 8x + y = 25 is ____________ .

## Very Short Type Questions

Q1: In Fig., ABCD is a rectangle. Find the values of x and y.

Q2: Name the geometrical figure enclosed by graph of the equations x + 7 = 0, y – 2 = 0 and x – 2 = 0, y + 7 = 0.
Q3: If 51x + 23y = 116 and 23x + 51y = 106, then find the value of (x – y).
Q4: For what value of V does the point (3, a) lie on the line represented by 2x – 3y = 5?
Q5: Determine whether the following system of linear equations is inconsistent or not.
3x – 5y = 20
6x – 10y = -40

Q1: The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. Find the present ages of the son and the father.

Q2: If the lines x + 2y + 7 = 0 and 2x + ky + 18 = 0 intersect at a point, then find the value of k.

Q3:  Find the value of k for which the system of equations x + 2y -3 = 0 and ky + 5x + 7 = 0 has a unique solution.

Q4: Find the values of a and b for which the following system of linear equations has an infinite number of solutions:
2x + 3 y = 7
2αx + (a + b) y = 28

Q5: In a cyclic quadrilateral ABCD, Find the four angles.
a. ∠A = (2 x + 4), ∠B = (y + 3), ∠C = (2y + 10) , ∠D = (4x − 5) .
b. ∠A = (2 x − 1) , ∠ B = (y + 5) , ∠C = (2 y + 15) and ∠D = (4 x − 7)

Q1: Draw the graph of 2x + y = 6 and 2x – y + 2 = 0. Shade the region bounded by these lines and the x-axis. Find the area of the shaded region.
Q2: Draw the graphs of the following equations:
2x – y = 1, x + 2y = 13
(i) Find the solution of the equations from the graph.
(ii) Shade the triangular region formed by lines and the y-axis.

Q3: A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.
Q4: The taxi charges in a city comprise a fixed charge together with the charge for the distance covered. For a journey of 10 km, the charge paid is ₹75 and for a journey of 15 km, the charge paid is ₹110. What will a person have to pay for traveling a distance of 25 km?
Q5: Solve the following system by drawing their graph:
32(3/2)x – (5/4)y = 6, 6x – 6y = 20.
Determine whether these are consistent, inconsistent, or dependent.

The document Pair of Linear Equations in Two Variables Class 10 Worksheet Maths Chapter 3 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Pair of Linear Equations in Two Variables Class 10 Worksheet Maths Chapter 3

 1. What are pair of linear equations in two variables?
Ans. Pair of linear equations in two variables is a system of two equations in which both equations are linear and contain two variables. These equations are usually represented as follows: a1x + b1y = c1 a2x + b2y = c2 where x and y are the variables and a1, a2, b1, b2, c1, and c2 are constants.
 2. How can we solve a pair of linear equations in two variables?
Ans. There are multiple methods to solve a pair of linear equations in two variables. Some common methods include: - Substitution Method: In this method, we solve one equation for one variable and substitute its value in the other equation to find the value of the second variable. - Elimination Method: In this method, we manipulate the equations to eliminate one variable by adding or subtracting the equations. Once one variable is eliminated, we can solve for the remaining variable. - Graphical Method: In this method, we plot the equations on a graph and find the point where the two lines intersect. The coordinates of the intersection point give the solution to the pair of linear equations.
 3. What is the significance of solving a pair of linear equations in two variables?
Ans. Solving a pair of linear equations in two variables has several significance. It helps in finding the values of the variables that satisfy both equations simultaneously. This can be used to solve real-life problems involving two unknowns. For example, it can be used to calculate the cost and quantity of two different items, find the intersection point of two moving objects, or determine the break-even point in business.
 4. Can a pair of linear equations in two variables have no solution?
Ans. Yes, a pair of linear equations in two variables can have no solution. This occurs when the two lines represented by the equations are parallel and do not intersect. In such cases, the equations are inconsistent, and there is no common solution that satisfies both equations simultaneously.
 5. Can a pair of linear equations in two variables have infinitely many solutions?
Ans. Yes, a pair of linear equations in two variables can have infinitely many solutions. This occurs when the two lines represented by the equations are coincident or overlapping. In such cases, the equations are dependent, and every point on the common line is a solution to the pair of equations.

## Mathematics (Maths) Class 10

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