Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Unit Test: Pair of Linear Equations in Two Variables
Unit Test: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10 PDF Download
Time: 1 hour
M.M. 30
Attempt all questions.
- Question numbers 1 to 5 carry 1 mark each.
- Question numbers 6 to 8 carry 2 marks each.
- Question numbers 9 to 11 carry 3 marks each.
- Question number 12 & 13 carry 5 marks each.
Q1: Which of the following options represents a pair of linear equations in two variables? (1 Mark)
(a) 2x + 3y = 7
(b) x2 + y2 = 25
(c) 4x + 2y = 10
(d) 3x + 2y2 = 8
Ans: (a)
Q2: The number of solutions for a pair of linear equations in two variables can be: (1 Mark)
(a) One
(b) Two
(c) Three
(d) None
Q3: If two lines represented by a pair of linear equations are parallel, then: (1 Mark)
(a) They intersect at one point
(b) They do not intersect
(c) They intersect at two points
(d) None of the above
Q4: Solve the pair of equations: 2x - 3y = 7 and 4x - 6y = 14. (1 Mark)
Q5: Check the consistency of the pair of linear equations and solve them graphically: (1 Mark)
4x - 3y = 9
8x - 6y = 18
Q6: Solve the pair of linear equations: (2 Marks)
x - y = 4
2x + 3y = 10
Q7: Find the value of 'k' for which the following system of equations has no solution: (2 Marks)
2x + 3y = 5
4x + ky = 10
Q8: A sum of money amounts to Rs. 11,000 after 3 years and Rs. 13,750 after 5 years, when it is invested at a certain rate of simple interest. Calculate the rate of interest using a pair of linear equations in two variables. (2 Marks)
Q9: The sum of the digits of a two-digit number is 9. If we add 9 to the number, the digits get reversed. Find the number using a pair of linear equations in two variables. (3 Marks)
Q10: Solve the following system of equations using any appropriate method: (3 Marks)
3x - 2y = 8
6x - 4y = 16
Q11: Solve the pair of linear equations: (3 Marks)
2x + y = 7
x - 3y = -4
Q12: The perimeter of a rectangle is 46 meters. The length is 4 meters more than twice the width. Find the dimensions of the rectangle using a pair of linear equations. (5 Marks)
Q13: A two-digit number is 6 times the sum of its digits. If 9 is added to the number, the digits interchange their places. Find the number using a pair of linear equations. (5 Marks)
You can find the solutions of this Unit Test here: Unit Test (Solutions): Pair of Linear Equations in Two Variables
The document Unit Test: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Unit Test: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10
| 1. What are linear equations in two variables? |  |
Ans. Linear equations in two variables are mathematical expressions that represent a straight line when graphed on a coordinate plane. They typically take the form Ax + By = C, where A, B, and C are constants, and x and y are variables. Each equation represents a line, and the solution to a pair of these equations is the point where the two lines intersect.
| 2. How can I solve a pair of linear equations? | |
Ans. A pair of linear equations can be solved using various methods such as substitution, elimination, or graphing. In the substitution method, you solve one equation for one variable and substitute that expression into the other equation. In the elimination method, you manipulate the equations to eliminate one variable, allowing you to solve for the other. Graphing involves plotting both equations on a graph and identifying their intersection point.
| 3. What is the graphical representation of a pair of linear equations? | |
Ans. The graphical representation of a pair of linear equations consists of two straight lines on a Cartesian plane. The point where the two lines intersect represents the solution to the equations, showing the values of the variables that satisfy both equations simultaneously. If the lines are parallel, there is no solution, and if they coincide, there are infinitely many solutions.
| 4. What are the types of solutions for linear equations in two variables? | |
Ans. There are three types of solutions for linear equations in two variables: a unique solution, no solution, and infinitely many solutions. A unique solution occurs when the two lines intersect at a single point. No solution happens when the lines are parallel and never intersect. Infinitely many solutions occur when the lines coincide, meaning they are the same line.
| 5. How do I check if my solution to a pair of linear equations is correct? | |
Ans. To check if your solution is correct, substitute the values of the variables back into both original equations. If both equations hold true with the substituted values, then your solution is correct. If either equation does not hold true, then the solution is incorrect, and you may need to re-evaluate your calculations.
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