NCERT Exemplar Class 10 Maths Unit 3 Pair of Linear Equations in Two Variables

Candidates can download NCERT Exemplar Class 10 Maths Unit 3 from this page. The exemplar has been provided by the National Council of Educational Research & Training (NCERT) and the candidates can check it from below for free of cost. It contains objective, very short answer type, short answer type, and long answer type questions. Along with it, the answer for each question has also been provided. From the NCERT Exemplar Class 10 Maths Unit 3, candidates can understand the level and type of questions that are asked in the exam.

NCERT Exemplar Class 10 Maths Unit 3 Pair of Linear Equations in Two Variables

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NCERT Class 10 Maths Unit 3 is for Pair of Linear Equations in Two Variables. The type of questions that will be asked from NCERT Class 10 Maths Unit 3 are displayed in the below provided NCERT Exemplar Class 10 Maths Unit 3. With the help of it, candidates can prepare well for the examination.

Main Concepts and Results

The pair of linear equations can also be solved geometrically/graphically.

Multiple Choice Questions (Solved Examples)

Multiple Choice Questions (Exercise)

Exercise- 3.1

6. For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16 represent coincident lines?

Short Answer Questions with Reasoning (Solved Examples)

Short Answer Questions with Reasoning (Exercise)

Exercise- 3.2

Short Answer Type Questions (Solved Examples)

We observe that there is a point R (2, 4) common to both the lines AB and PQ.
The triangle formed by these lines and the x- axis is BQR.
The vertices of this triangle are B (–2, 0), Q (1, 0) and R (2, 4).
We know that;

Short Answer Type Questions (Exercise)

Exercise- 3.3

Long Answer Type Questions (Solved Examples)

C is a point on the x-axis at a distance of 2 units to the left of y-axis. So, the coordinates of C are (–2, 0)
B is the solution of the pair of equations x = –2 and y = 3. So, the coordinates of B are (–2, 3) So, the vertices of the rectangle OABC are O (0, 0), A (0, 3), B (–2, 3), C (–2, 0)
The length and breadth of this rectangle are 2 units and 3 units, respectively.
As the area of a rectangle = length × breadth,
the area of rectangle OABC = 2 × 3 = 6 sq. units.
Sample Question 2: Determine, algebraically, the vertices of the triangle formed by the lines
5x – y = 5, x + 2y = 1 and 6x + y = 17.

5x – y = 5
6x + y = 17,
we get x = 2, y = 5.
So, the third vertex of the triangle is (2, 5). So, the three vertices of the triangle are
(1, 0), (3, –1) and (2, 5).
Sample Question 3: Jamila sold a table and a chair for Rs 1050, thereby making a profit
of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and
10% on the chair she would have got Rs 1065. Find the cost price of each.
Solution: Let the cost price of the table be Rs x and the cost price of the chair be Rs y.