SEBA Class 9 Maths Linear Equations in Two Variables MCQs (2026–27) – Assam Eduverse
The SEBA Class 9 Maths Linear Equations in Two Variables MCQs (2026–27) are prepared according to the latest ASSEB syllabus and the updated board exam pattern. These SEBA Class 9 Maths Linear Equations in Two Variables MCQs include conceptual objective questions, algebra-based MCQs, and graph-related practice questions designed for board exam preparation.
Prepared by subject experts of Assam Eduverse, these practice questions focus on important topics such as the concept of linear equations, standard form of linear equations, graphical representation of equations, solutions of equations in two variables, and real-life applications. Practicing linear equations in two variables mcqs class 9 seba and assam board class 9 maths objective questions helps students strengthen algebraic understanding and mathematical reasoning.
Regular revision of these ASSEB class 9 maths important MCQs improves conceptual clarity and helps students perform confidently in the 2026–27 board examination.
SEBA Class 9 Maths Linear Equations in Two Variables MCQs – ASSEB Board Exam Practice
Table of Contents
Q1. The solution of the equation x – 2y = 4 is:
(a) (0, 2)
(b) (4, 0)
(c) (1, 1)
(d) (2, 0)
Answer: (b) (4, 0)
Substitute each option in x – 2y = 4.
For (4, 0): 4 – 2(0) = 4 ✔
So, (4, 0) satisfies the equation.
Q2. In graphical representation of y = –4, line is:
(a) parallel to x – axis
(b) parallel to y – axis
(c) passes through origin
(d) None of these
Answer: (a) parallel to x – axis
y = –4 means y is constant.
A line with constant y is parallel to x-axis.
Q3. Solution of the equation 2x + 1 = x + 3 is:
(a) 3
(b) 1
(c) 2
(d) 4
Answer: (c) 2
2x + 1 = x + 3
2x – x = 3 – 1
x = 2
Q4. The graph of line x – y = 0 passes through:
(a) (2, 3)
(b) (3, 4)
(c) (5, 6)
(d) (0, 0)
Answer: (d) (0, 0)
x – y = 0 ⇒ x = y
At (0, 0), 0 – 0 = 0 ✔
So it passes through (0, 0).
Q5. The graph of line x + y = 7 intersect the x-axis at:
(a) (7, 0)
(b) (0, 7)
(c) (–7, 0)
(d) (0, –7)
Answer: (a) (7, 0)
On x-axis, y = 0.
x + 0 = 7 ⇒ x = 7
So, point is (7, 0).
Q6. Point (4, 1) lies on the line:
(a) x + 2y = 5
(b) x + 2y = –6
(c) x + 2y = 6
(d) x + 2y = 16
Answer: (a) x + 2y = 5
Substitute (4,1):
x + 2y = 4 + 2(1) = 6
So correct equation is x + 2y = 6.
Hence option (c).
Q7. Graph of x = 2 is a line:
(a) parallel to x – axis
(b) parallel to y – axis
(c) passes through origin
(d) None of these
Answer: (b) parallel to y – axis
x = 2 means x is constant.
A line with constant x is parallel to y-axis.
Q8. The linear equation 2x – 5y = 7 has:
(a) a unique solution
(b) two solutions
(c) infinitely many solutions
(d) no solutions
Answer: (c) infinitely many solutions
A linear equation in two variables represents a line.
A line has infinitely many points.
So, infinitely many solutions.
Q9. The equation 2x + 5y = 7 has a unique solution, if x, y are:
(a) natural numbers
(b) positive numbers
(c) real numbers
(d) rational numbers
Answer: (a) natural numbers
In real or rational numbers, equation has infinitely many solutions.
In natural numbers, only one pair (1,1) satisfies:
2(1) + 5(1) = 7
So unique solution in natural numbers.
Q10. If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is:
(a) 4
(b) 6
(c) 5
(d) 2
Answer: (a) 4
Substitute (2,0):
2(2) + 3(0) = 4
So, k = 4.
Q11. Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form:
(a) (–9/2, m)
(b) (n, –9/2)
(c) (0, –9/2)
(d) (–9, 0)
Answer: (a) (–9/2, m)
2x + 9 = 0
2x = –9
x = –9/2
y can be any value (m).
So solution is (–9/2, m).
Q12. The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point:
(a) (2, 0)
(b) (0, 3)
(c) (3, 0)
(d) (0, 2)
Answer: (d) (0, 2)
On y-axis, x = 0.
2(0) + 3y = 6
3y = 6
y = 2
So point is (0, 2).
Q13. The equation x = 7, in two variables, can be written as:
(a) x + 0y = 7
(b) 0x + y = 7
(c) 0x + 0y = 7
(d) x + y = 7
Answer: (a) x + 0y = 7
x = 7 can be written as x + 0y = 7.
Q14. Any point on the x – axis is of the form:
(a) (x, y)
(b) (0, y)
(c) (x, 0)
(d) (x, x)
Answer: (c) (x, 0)
On x-axis, y = 0.
So any point is (x, 0).
Q15. Any point on the y = x is of the form:
(a) (a, a)
(b) (0, a)
(c) (a, 0)
(d) (a, –a)
Answer: (a) (a, a)
On the line y = x, the value of y is equal to x.
So any point will be of the form (a, a).
Q16. The equation of x – axis is of the form:
(a) x = 0
(b) y = 0
(c) x + y = 0
(d) x = y
Answer: (b) y = 0
On the x-axis, the y-coordinate is always 0.
So its equation is y = 0.
Q17. Graph of y = 6 is a line:
(a) parallel to x – axis at a distance 6 units from the origin
(b) parallel to y – axis at a distance 6 units from the origin
(c) making an intercept 6 on the x–axis
(d) making an intercept 6 on both the axes
Answer: (a) parallel to x – axis at a distance 6 units from the origin
y = 6 means y is constant.
So the line is parallel to x-axis.
It is 6 units above the origin.
Q18. x = 5, y = 2 is a solution of the linear equation:
(a) x + 2y = 7
(b) 5x + 2y = 7
(c) x + y = 7
(d) 5x + y = 7
Answer: (a) x + 2y = 7
Substitute x = 5, y = 2:
x + 2y = 5 + 2(2) = 5 + 4 = 9 (not 7) ✖
5x + 2y = 25 + 4 = 29 ✖
x + y = 5 + 2 = 7 ✔
So correct answer is (c).
Q19. If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form:
(a) y – x = 0
(b) x + y = 0
(c) –2x + y = 0
(d) –x + 2y = 0
Answer: (b) x + y = 0
For (–2, 2): –2 + 2 = 0 ✔
For (0, 0): 0 + 0 = 0 ✔
For (2, –2): 2 – 2 = 0 ✔
So equation is x + y = 0.
Q20. The positive solutions of the equation ax + by + c = 0 always lie in the:
(a) 1st quadrant
(b) 2nd quadrant
(c) 3rd quadrant
(d) 4th quadrant
Answer: (a) 1st quadrant
Positive solutions mean x > 0 and y > 0.
Such points lie in the first quadrant.
Q21. The graph of the linear equation 2x + 3y = 6 is a line which meets the x–axis at the point:
(a) (2, 0)
(b) (0, 3)
(c) (3, 0)
(d) (0, 2)
Answer: (c) (3, 0)
On x-axis, y = 0.
2x + 3(0) = 6
2x = 6
x = 3
So point is (3, 0).
Q22. The graph of y = x passes through the point:
(a) (3/2, –3/2)
(b) (0, 3/2)
(c) (1, 1)
(d) (–1/2, 1/2)
Answer: (c) (1, 1)
On y = x, y must equal x.
Only (1, 1) satisfies this condition.
Q23. If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:
(a) changes
(b) remains the same
(c) changes in case of multiplication only
(d) changes in case of division only
Answer: (b) remains the same
Multiplying or dividing both sides by a non-zero number
does not change the solution of the equation.
Q24. How many linear equation in x and y can be satisfied by x = 1 and y = 2?
(a) only one
(b) two
(c) infinitely many
(d) three
Answer: (c) infinitely many
We can form infinitely many equations like:
x + y = 3, 2x + y = 4, x + 2y = 5, etc.
All are satisfied by (1, 2).
So infinitely many equations.
Q25. The point of the form (a, a) always lies on:
(a) x – axis
(b) y – axis
(c) on the line y = x
(d) on the x + y = 0
Answer: (c) on the line y = x
In (a, a), x = y.
So it lies on y = x.
Q26. The point of the form (a, –a) always lies on:
(a) x = a
(b) y = –a
(c) y = x
(d) x + y = 0
Answer: (d) x + y = 0
For point (a, –a):
x + y = a + (–a) = 0
So it lies on x + y = 0.
Q27. Which of the following is not a linear equation in two variables?
(a) ax + by = c
(b) ax² + by = c
(c) 2x + 3y = 5
(d) 3x + 2y = 6
Answer: (b) ax² + by = c
A linear equation has variables of degree 1 only.
In ax² + by = c, x has power 2.
So it is not a linear equation.
Q28. The graph of ax + by + c = 0 is:
(a) a straight line parallel to x–axis
(b) a straight line parallel to y–axis
(c) a general straight line
(d) a line in the 2nd and 3rd quadrant
Answer: (c) a general straight line
ax + by + c = 0 represents a straight line.
It is the general form of a linear equation in two variables.
Q29. The solution of a linear equation in two variables is:
(a) a number which satisfies the given equation
(b) an ordered pair which satisfies the given equation
(c) an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it
(d) none of these
Answer: (c) an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it
A solution must satisfy the equation when we substitute x and y.
So it must be an ordered pair (x, y) that makes the equation true.
Q30. One of the solution of a linear equation in two variables is:
(a) (3, 2)
(b) (3, –2)
(c) (2, 3)
(d) (–2, –3)
Answer: (a) (3, 2)
An ordered pair like (3, 2) is an example of a solution
for some linear equation in two variables.
Q31. The ordered pair (m, n) satisfies the equation ax + by + c = 0 if:
(a) am + bn = 0
(b) c = 0
(c) am + bn + c = 0
(d) am + bn – c = 0
Answer: (c) am + bn + c = 0
Substitute x = m and y = n in ax + by + c = 0:
am + bn + c = 0
So option (c) is correct.
Q32. The equation of x – axis is:
(a) a = 0
(b) y = 0
(c) x = 0
(d) y = k
Answer: (b) y = 0
On the x-axis, y-coordinate is always 0.
So its equation is y = 0.
Q33. From the graph of a line, we can find the coordinates of:
(a) only two points lying on the line
(b) only two points only lying on the line
(c) only finite number of points lying on the line
(d) only infinite number of points lying on the line
Answer: (d) only infinite number of points lying on the line
A straight line contains infinitely many points.
So we can find infinitely many coordinates from its graph.
Q34. A linear equation in two variables has:
(a) no solution
(b) only one solution
(c) only two solutions
(d) infinitely many solutions
Answer: (d) infinitely many solutions
A linear equation in two variables represents a straight line.
A straight line has infinitely many points.
So it has infinitely many solutions.
Q35. An equation of the form ax + by + c = 0 represents a linear equation in two variables, if:
(a) a = 0, b ≠ 0
(b) a ≠ 0, b = 0
(c) a = 0, b = 0
(d) a ≠ 0, b ≠ 0
Answer: (d) a ≠ 0, b ≠ 0
For ax + by + c = 0 to represent a linear equation in two variables,
both coefficients of x and y should not be zero simultaneously.
So a ≠ 0 and b ≠ 0.
Q36. The graph of the linear equation in two variables y = mx is:
(a) a line parallel to x – axis
(b) a line parallel to y – axis
(c) a line passing through the origin
(d) not a straight line
Answer: (c) a line passing through the origin
In y = mx, when x = 0, y = 0.
So the line passes through the origin.
It is a straight line.
SEBA Class 9 Maths Linear Equations in Two Variables MCQs (2026–27) Important Objective Questions
The SEBA Class 9 Maths Linear Equations in Two Variables MCQs provided here are prepared according to the latest ASSEB syllabus 2026–27. These questions include conceptual objective questions and exam-oriented practice sets designed for effective board exam preparation.
Students preparing for the board examination should regularly practice SEBA Class 9 Maths Linear Equations in Two Variables MCQs. These practice questions cover important topics such as standard form of linear equations, graphical representation of equations, solutions of equations in two variables, and algebraic interpretation of graphs.
The linear equations in two variables mcqs class 9 seba are prepared by subject experts to ensure alignment with the latest examination pattern. These ASSEB class 9 maths important MCQs help students understand equation solving methods and graphical concepts clearly.
Regular revision using SEBA Class 9 Maths Linear Equations in Two Variables MCQs along with assam board class 9 maths objective questions improves algebraic reasoning, graph interpretation skills, and overall board exam performance.
Frequently Asked Questions (FAQ)
1. Are these SEBA Class 9 Maths Linear Equations in Two Variables MCQs based on the latest syllabus?
Yes, these MCQs are prepared strictly according to the latest ASSEB syllabus for the 2026–27 academic session.
2. Are linear equations in two variables mcqs class 9 seba helpful for exam preparation?
Yes, these MCQs are designed according to the latest board exam pattern and help students practice important algebra questions.
3. Do these questions include graph-based problems?
Yes, the questions include graph-related problems and conceptual algebra questions based on linear equations.
4. Who prepared these ASSEB class 9 maths important MCQs?
These MCQs are prepared by subject experts of Assam Eduverse according to the updated board syllabus.
5. Are assam board class 9 maths objective questions from this topic important?
Yes, objective questions from linear equations are commonly asked in Assam Board Class 9 Mathematics exams.
6. Which topics are covered in Linear Equations MCQs?
Topics include standard form of equations, graphical representation, and solutions of equations in two variables.
7. Can practicing MCQs improve maths exam performance?
Yes, regular practice improves algebraic reasoning, graph interpretation skills, and exam confidence.
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