Chapter 4, Linear Equations in Two Variables, introduces students to equations like ax + by + c = 0 and their infinite solutions. It connects algebra to geometry, demonstrating how such equations form straight lines on a Cartesian plane. This set includes 32 MCQs that cover key concepts like identifying equations, solving for variables, and interpreting solutions. These questions aim to build problem-solving skills and bridge classroom learning with real-life applications.
Class 9th Maths Important MCQs with Answers from Chapter 4 – Linear Equations in Two Variables
Question 1. Which of the following is the general form of a linear equation in two variables?
a) ax + by = c
b) ax + by + c = 0
c) ax – by = 0
d) ax + c = 0
Answer:
b) ax + by + c = 0 – The standard form is ax + by + c = 0, where a and b are not both zero.
Question 2. Which of the following equations is NOT linear in two variables?
a) 2x + 3y = 6
b) 4x – 5 = 0
c) xy = 7
d) x + 0.y = 2
Answer:
c) xy = 7 – This is not linear because the product xy makes it quadratic-like.
Question 3. The equation 4 – 3x = 0 can be written as:
a) 3x + 4 = 0
b) –3x + 4 = 0
c) –3x + 0.y + 4 = 0
d) 4x – 3 = 0
Answer:
c) –3x + 0.y + 4 = 0 – It is expressed in two-variable form with coefficient of y as 0.
Question 4. The equation y = 2 can be expressed in two-variable form as:
a) y – 2 = 0
b) 0.x + y – 2 = 0
c) x + y = 2
d) 2x + y = 0
Answer:
b) 0.x + y – 2 = 0 – This fits ax + by + c = 0 form with a = 0, b = 1, c = –2.
Question 5. Which of these is a solution of 2x + 3y = 12?
a) (3, 2)
b) (2, 3)
c) (4, 0)
d) (0, 2)
Answer:
a) (3, 2) – Substituting gives 2(3) + 3(2) = 12.
Question 6. The equation 5y = 2 can be written in standard form as:
a) y = 2/5
b) 0.x + 5y – 2 = 0
c) 5y – 2 = 0
d) x + 5y = 2
Answer:
b) 0.x + 5y – 2 = 0 – Fits ax + by + c = 0 with a = 0, b = 5, c = –2.
Question 7. Which of these points is a solution of x – 2y = 4?
a) (0, 2)
b) (2, 0)
c) (4, 0)
d) (1, 1)
Answer:
c) (4, 0) – Substituting: 4 – 2(0) = 4.
Question 8. A linear equation in two variables has how many solutions?
a) None
b) One
c) Two
d) Infinitely many
Answer:
d) Infinitely many – Every linear equation in two variables has infinite solutions.
Question 9. The equation 3x + 2 = 0 can be expressed as:
a) 3x + 0.y + 2 = 0
b) 3x + 2y = 0
c) x + y = –2
d) 2x + y = 0
Answer:
a) 3x + 0.y + 2 = 0 – Standard form with coefficient of y = 0.
Question 10. Which of the following ordered pairs is NOT a solution of 2x + y = 7?
a) (2, 3)
b) (1, 5)
c) (3, 1)
d) (0, 7)
Answer:
c) (3, 1) – Substituting gives 2(3)+1=7, which is false (it gives 7 ≠ 7).
Question 11. The equation x = –5 can be written as:
a) x + 5 = 0
b) 1.x + 0.y + 5 = 0
c) x – 5 = 0
d) –x + 5 = 0
Answer:
b) 1.x + 0.y + 5 = 0 – In ax + by + c = 0 form.
Question 12. The cost of a notebook is twice the cost of a pen. If notebook cost = x and pen cost = y, the equation is:
a) x = y/2
b) x = 2y
c) y = 2x
d) x + y = 2
Answer:
b) x = 2y – Notebook cost is twice pen’s cost.
Question 13. If 2x + 3y = k and (2, 1) is a solution, then k = ___.
a) 5
b) 7
c) 8
d) 10
Answer:
c) 7 – Substituting: 2(2) + 3(1) = 7.
Question 14. Which of these represents a vertical line on the Cartesian plane?
a) y = 3
b) x = 4
c) y = 2x
d) y = x + 1
Answer:
b) x = 4 – Equation x = constant represents a vertical line.
Question 15. Which of these represents a horizontal line on the Cartesian plane?
a) x = 2
b) y = –5
c) 2x + y = 3
d) y = x
Answer:
b) y = –5 – Equation y = constant represents a horizontal line.
Question 16. Which one of the following is true for the equation y = 3x + 5?
a) Unique solution
b) Only two solutions
c) Infinitely many solutions
d) No solution
Answer:
c) Infinitely many solutions – Each value of x gives a corresponding y.
Question 17. The graph of a linear equation in two variables is always a:
a) Straight line
b) Curve
c) Circle
d) Hyperbola
Answer:
a) Straight line – A linear equation always represents a line.
Question 18. The equation 2x = –5y can be expressed as:
a) 2x + 5y = 0
b) 2x – 5y = 0
c) x + y = 0
d) 2x + y = –5
Answer:
a) 2x + 5y = 0 – Rearranging gives the standard form.
Question 19. Which of these points is a solution of 2x + 5y = 0?
a) (1, 2)
b) (0, 0)
c) (2, 1)
d) (–5, 2)
Answer:
b) (0, 0) – Substituting gives 0 = 0.
Question 20. The equation 3y + 4 = 0 can be written as:
a) 3y = –4
b) 0.x + 3y + 4 = 0
c) y = –4/3
d) All of the above
Answer:
d) All of the above – All forms represent the same equation.
Question 21. The solution (6, 0) belongs to which equation?
a) x + y = 6
b) 2x + 3y = 12
c) x – 2y = 4
d) y = x + 6
Answer:
b) 2x + 3y = 12 – Substituting gives 12 = 12.
Question 22. Which of the following pairs is NOT a solution of x + 2y = 6?
a) (2, 2)
b) (0, 3)
c) (6, 0)
d) (4, 2)
Answer:
d) (4, 2) – Substituting gives 4 + 4 = 8 ≠ 6.
Question 23. The ordered pair (4, 1) is a solution of:
a) x + 2y = 6
b) 2x + 3y = 12
c) y = x – 3
d) x – y = 2
Answer:
a) x + 2y = 6 – Substituting gives 4 + 2 = 6.
Question 24. Which line represents the equation y = 0?
a) x-axis
b) y-axis
c) Origin
d) Line x = 0
Answer:
a) x-axis – The line y = 0 coincides with x-axis.
Question 25. The line x = 0 represents which axis?
a) x-axis
b) y-axis
c) Origin
d) z-axis
Answer:
b) y-axis – Equation x = 0 coincides with y-axis.
Question 26. Which point does NOT satisfy y = x?
a) (1, 1)
b) (2, 2)
c) (3, 4)
d) (–1, –1)
Answer:
c) (3, 4) – Here y ≠ x.
Question 27. The line y = 2x passes through which point?
a) (1, 2)
b) (2, 5)
c) (3, 8)
d) (–1, –1)
Answer:
a) (1, 2) – Substituting satisfies y = 2x.
Question 28. The equation of the x-axis is:
a) x = 0
b) y = 0
c) x + y = 0
d) None
Answer:
b) y = 0 – The x-axis is defined by y = 0.
Question 29. The equation of the y-axis is:
a) y = 0
b) x = 0
c) x + y = 0
d) None
Answer:
b) x = 0 – The y-axis is defined by x = 0.
Question 30. The equation of a line parallel to x-axis at distance 3 units is:
a) y = 3
b) x = 3
c) y = –3
d) Both a and c
Answer:
d) Both a and c – y = 3 and y = –3 are parallel to x-axis.
Question 31. The equation of a line parallel to y-axis at distance 4 units is:
a) y = 4
b) x = 4
c) x = –4
d) Both b and c
Answer:
d) Both b and c – x = 4 and x = –4 are parallel to y-axis.
Question 32. Which equation has solutions of the form (x, –1)?
a) y = –1
b) x = –1
c) y = x
d) x + y = 0
Answer:
a) y = –1 – Any point with ordinate –1 satisfies this line.
Question 33. Which of the following represents a line passing through origin?
a) y = x
b) y = 2x + 3
c) x + y = 5
d) y = –x + 4
Answer:
a) y = x – Line y = x passes through (0, 0).
Question 34. If a line passes through (0, –4), which equation can represent it?
a) y = –4
b) x = –4
c) y = x – 4
d) y = –x – 4
Answer:
a) y = –4 – The line y = –4 passes through (0, –4).
Question 35. The graph of x + y = 0 is a line that passes through:
a) Only x-axis
b) Only y-axis
c) Both axes (origin)
d) Neither axis
Answer:
c) Both axes (origin) – It passes through (0, 0) and lies symmetrically in opposite quadrants.
Fill in the blanks on Linear Equations in Two Variables for Class 9 Maths
1. Any equation of the form ax + by + c = 0, where a and b are not both zero, is called a ___.
Answer:
Linear equation in two variables
2. The equation 2x + 5 = 0 is a linear equation in ___ variable.
Answer:
one
3. The equation x + y = 176, where x and y are runs scored by two batsmen, is an example of a linear equation in ___ variables.
Answer:
two
4. The equation 2x + 3y – 12 = 0 is written in the general form ax + by + c = 0, where a = ___, b = ___, c = ___.
Answer:
2, 3, –12
5. The equation y = 2 can be written in standard form as 0.x + 1.y – ___ = 0.
Answer:
2
6. The equation x = –5 can be written in the form 1.x + 0.y + ___ = 0.
Answer:
5
7. The equation 2x = y can be rewritten as 2x – y + ___ = 0.
Answer:
0
8. The solution of a linear equation in two variables is written as an ordered pair ___.
Answer:
(x, y)
9. The pair (3, 2) is a solution of 2x + 3y = 12 because substituting gives 2(3) + 3(2) = ___.
Answer:
12
10. The point (1, 4) is NOT a solution of 2x + 3y = 12 because it gives a value of ___ instead of 12.
Answer:
14
11. A linear equation in two variables has ___ many solutions.
Answer:
Infinitely
12. The ordered pair (0, 4) is a solution of 2x + 3y = 12 because substituting gives ___ = 12.
Answer:
3(4)
13. The solution (6, 0) satisfies 2x + 3y = 12 because substituting gives 2(6) + 3(0) = ___.
Answer:
12
14. If y = 0 in the equation x + 2y = 6, then x = ___.
Answer:
6
15. If x = 0 in the equation x + 2y = 6, then y = ___.
Answer:
3
16. For the equation 2x + 5y = 0, if x = 1, then y = ___.
Answer:
–2/5
17. The line x = –5 represents a line ___ to the y-axis.
Answer:
parallel
18. The line y = 2 represents a line ___ to the x-axis.
Answer:
parallel
19. Every point on the graph of a linear equation in two variables is a ___ of the equation.
Answer:
solution
20. The graph of any linear equation in two variables is always a ___ line.
Answer:
straight
21. The line y = 0 represents the ___ axis of the Cartesian plane.
Answer:
x-
