### Class 10 Maths Objective Questions Chapter 3 Pair Of Linear Equations In Two Variables

CBSE Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Objective Questions

Chapter 3- Pair of Linear Equations in Two Variables from CBSE Class 10 Maths textbook explains all about the pair of linear equations in two variables. Two linear equations in two variables also called the pair of linear equations in two variables can be represented graphically and algebraically. Algebraically, students can use the Substitution method, Elimination method or Cross-multiplication method to solve the pair of linear equations in two variables.

From this chapter, we have compiled some 20 MCQs, which have been categorized topic-wise in the PDF link given below:

Some of the main sub-topics covered in this chapter of the CBSE Class 10 Maths have been listed below. Students also find these CBSE Class 10 Maths Objective Questions very useful. Students can practice the MCQs from the chapter given topic wise and master the concepts from the topics of this chapter. Here are the list of topics given:

3.1 Algebraic Solution (4 MCQs Listed From This Topic)

3.2 All about Lines (4 MCQs From The Topic)

3.3 Basics Revisited (4 MCQs From This Topic)

3.4 Graphical Solution (4 MCQs Listed From The Topic)

3.5 Solving Linear Equations (4 MCQs From The Mentioned Topic)

Solution: Let l and b be the length and breadth of the room. Then, the perimeter of the room = 2(l+b) metres

Substituting the value of l from (1) in (2), we get

Choose the correct answer from the given options.

Multiply equation (1) by 2, we get:

Substituting the value of x in (1) we get,

Thus, the solution for the given pair of linear equations is (2, 3).

LCM of 2 and 3 is 6. Multiply by 6 on both sides

LCM is 6. Multiply by 6 on both sides

Multiply equation (2) by 3 to eliminate x; so we get,

Substitute this in one of the equation and we get

Solve above equations by Elimination method and find the value of x.

Solution: For a pair of equations to satisfy a point, the point should be the unique solution of them.

Solve the pair equations 4x+y=3,3x+2y=1

⇒ (1,-1) is the solution of pair of equation.

∴ Pair of equations which satisfy the point (1,-1)

Note: – We can also substitute the value (1,-1) in the given equations and check if it satisfies the pair of equations or not. In this case it only satisfies the pair of equation 4x+y=3, 3x+2y=1 and hence (1, -1) is the unique solution of the equation.

Solution: Let the 2 parts of 54 be x and y

Substituting y = 20 in x + y = 54, we have x + 20 = 54; x = 34

The general form of an equation is ax+by+c=0.

Solution: If two equations are consistent and overlapping, then they will have infinite solutions. Option A consists of two equations where the second equation can be reduced to an equation which is same as the first equation.

Dividing equation (ii) by 3, we get

x+2y=7 which is the same as equation (i).

The equations coincide and will have an infinite solution.

Solution : Substituting the value of x = 3 and y = 4,

Substituting the value of x = 2 and y = 5,

Substituting the value of x = -3 and y = 7,

Substituting the value of x = 3 and y = 5,

Hence, (3, 5) lies on the given line

Solution: Substituting the values in LHS,

Hence x=−3, y=2 is the solution of the equation 2x+3y=0

Thus, the value of a, b and c is -3, 2 and -7 respectively.

The equation can also be written as,

Thus, the value of a, b and c is +3, -2 and +7 respectively.

The option -3, 2 and -7 is correct [Since +3, -2 and +7 is not an option]

Solution: x−y=0, is a line passing through the origin as point (0, 0) satisfies the given equation

Statement 1: This is the condition for inconsistent equations

Statement 2: There exists infinitely many solutions

Statement 3: The equations satisfying the condition are parallel

Which of the above statements are true?

The condition is for inconsistent pair of equations which are parallel and have no solution.

Answer: For k= 5 (m/3), infinitely many solutions exist

Solution: If the graph of linear equations represented by the lines intersects at a point, this point gives the unique solution. Here the lines meet at the point (1,-1) which is the unique solution of the given pair of linear equations.

Solution: Given equations gives infinitely many solutions if,

Solution: The pair of equations is not linear. We will substitute 1/x as u 2 and 1/y as v 2 then we will get the equation as

We will use method of elimination to solve the equation.

Multiply the first equation by 3, we get

Substituting u in equation 4u−9v=−1 we get v= 1/3

Multiplying equation (1) by 4, we get 4a+12b=4 … (3)

On adding equation (2) and equation (3), we get 10a=6

Putting a= 3/5 in equation (1), we get

The students appearing for the board examinations will find it helpful in scoring well, as according to the latest modified exam pattern, the question paper will contain more objective type questions.

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