Looking for accurate SEBA Class 10 Maths Exercise 3.1 (Pair of Linear Equations in Two Variables) textual solutions for the 2026–27 academic year? Access complete step-by-step solutions covering word problem algebraic representations, graphical consistency tests, ratio comparisons a1/a2, b1/b2, c1/c2 (intersecting, parallel, and coincident lines), and graphical solutions to score full marks in your HSLC board exams.
1. Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
2. On comparing the ratios a1/a2, b1/b2, and c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0
(ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0
(iii) 6x – 3y + 10 = 0 2x – y + 9 = 0
3. On comparing the ratios a1/a2, b1/b2, and c1/c2, find out whether the following pair of linear equations are consistent, or inconsistent.
(i) 3x + 2y = 5; 2x – 3y = 7
(ii) 2x – 3y = 8; 4x – 6y = 9
(iii) 3/2 x + 5/3 y = 7; 9x – 10y = 14
(iv) 5x – 3y = 11; -10x + 6y = -22
(v) 4/3 x + 2y = 8; 2x + 3y = 12
SEBA Class 10 Maths Exercise 3.1 Solutions
4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
(i) x + y = 5, 2x + 2y = 10
(ii) x – y = 8, 3x – 3y = 16
(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
Class 10 Maths Chapter 3 Exercise 3.1 Question Answer SEBA 2026-27
5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Pair of Linear Equations Class 10 SEBA Ex 3.1 Solutions
6. Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines
7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
SEBA Class 10 Maths Chapter 3 Exercise 3.1 Textbook Answers
8. For what value of P does the pair of equations given below has unique solution?
4x + Py + 8 = 0
2x + 2y + 2 = 0
(a) when P = 4
(b) when P != 4
(c) when P = -4
(d) P != -4
9. Which of the following has infinitely many solutions?
(a) 2x + 3y = 6 and 4x + 6y – 12 = 0
(b) x + y = 4 and x – y – 2 = 0
(c) x – y = 3 and x + y = 7
(d) x + y = 5 and 2x – y = 3
10. In the following question a statement of assertion (A) is followed by a statement of reason (R).
Assertion (A): The equation 2x – 3y = 0 has an infinite number of solutions. Reason (R): A linear equation in two variables represents a straight line on the co-ordinate plane.
Choose the correct option from the given alternatives:
(a) Both assertion (A) and reason (R) are true and reason (R) is correct explanation of assertion (A) (b) Both assertion (A) and reason (R) are true and reason (R) is not correct explanation of assertion (A) (c) Assertion (A) is true, but reason (R) is false (d) Assertion (A) is false, but reason (R) is true
Class 10 Maths Graphical Representation Exercise 3.1 HSLC Solutions
📐 Updated Solutions Notice: This page features complete, step-by-step SEBA Class 10 Mathematics Chapter 3 (Pair of Linear Equations in Two Variables) Exercise 3.1 Textual Solutions updated for the 2026–27 academic session. All algebraic formulations, table creation for graph plotting, ratio comparisons, and graphical consistency checks strictly follow the latest revised Assam Board (SEBA) HSLC curriculum.
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