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 equations is a linear equation in two variables?
a) 3x + 5y = 7
b) x² + y = 4
c) x + y² = 9
d) xy = 6
Answer:
a) 3x + 5y = 7 — A linear equation in two variables is of the form ax + by + c = 0, where x and y have power 1.
Question 2. What is the standard form of a linear equation in two variables?
a) ax² + by + c = 0
b) ax + by + c = 0
c) ax + b = 0
d) x² + y² = 0
Answer:
b) ax + by + c = 0 — The standard form includes two variables with powers of 1.
Question 3. How many solutions does a linear equation in two variables have?
a) One
b) Two
c) Infinitely many
d) None
Answer:
c) Infinitely many — A linear equation in two variables has infinitely many solutions.
Question 4. Which of the following is an example of a linear equation in two variables?
a) x + y = 5
b) x² + y = 5
c) x + y² = 5
d) xy = 5
Answer:
a) x + y = 5 — It is in the form ax + by + c = 0, with variables having a power of 1.
Question 5. Which of the following is true about a linear equation in two variables?
a) It has one solution.
b) It has exactly two solutions.
c) It has no solution.
d) It has infinitely many solutions.
Answer:
d) It has infinitely many solutions — Any linear equation in two variables has an infinite number of solutions.
Question 6. If x + y = 10, which of the following is a solution?
a) (5, 5)
b) (3, 6)
c) (0, 0)
d) (7, 3)
Answer:
a) (5, 5) — Substitute x = 5 and y = 5: 5 + 5 = 10, so (5, 5) is a solution.
Question 7. What is the equation of a line passing through (0, 3) with a slope of 2?
a) y = 2x + 3
b) y = 3x + 2
c) y = x + 3
d) y = -2x + 3
Answer:
a) y = 2x + 3 — The equation in slope-intercept form is y = mx + c, where m = 2 and c = 3.
Question 8. What is the solution of 3x + y = 9 if x = 2?
a) (2, 3)
b) (2, -3)
c) (2, 2)
d) (2, 1)
Answer:
a) (2, 3) — Substitute x = 2: 3(2) + y = 9 → 6 + y = 9 → y = 3. The solution is (2, 3).
Question 9. Which of the following is a valid linear equation in two variables?
a) x² – y = 5
b) 2x + y = 6
c) x + y² = 3
d) x³ + y = 1
Answer:
b) 2x + y = 6 — It follows the form ax + by + c = 0, where x and y have power 1.
Question 10. If the cost of a pen is `x and the cost of a pencil is `y, which equation represents a total cost of `50 for 2 pens and 3 pencils?
a) 2x + 3y = 50
b) 2x – 3y = 50
c) x + y = 50
d) 3x + 2y = 50
Answer:
a) 2x + 3y = 50 — The total cost of 2 pens and 3 pencils is represented as 2x + 3y = 50.
Question 11. Which of the following is a linear equation in two variables?
a) 3x² + 2y = 5
b) x + y = 3
c) x² + y² = 1
d) 5xy = 10
Answer:
b) x + y = 3 — It is in the form ax + by + c = 0, with variables having a power of 1.
Question 12. If x = 0 and y = 5 is a solution of 2x – y = -5, what is another solution when y = 0?
a) (5, 0)
b) (0, -5)
c) (-5, 0)
d) (0, 5)
Answer:
c) (-5, 0) — Substitute y = 0: 2x – 0 = -5 → 2x = -5 → x = -5. The solution is (-5, 0).
Question 13. How many variables are there in the linear equation x + y = 7?
a) One
b) Two
c) Three
d) None
Answer:
b) Two — The equation x + y = 7 has two variables, x and y.
Question 14. Which of the following represents the equation of a vertical line?
a) y = 5
b) x = -3
c) y = x
d) x + y = 0
Answer:
b) x = -3 — An equation of the form x = constant represents a vertical line.
Question 15. What is the x-intercept of the line represented by the equation 2x + y = 6?
a) (0, 6)
b) (3, 0)
c) (0, 0)
d) (-3, 0)
Answer:
b) (3, 0) — Substitute y = 0: 2x + 0 = 6 → x = 3. The x-intercept is (3, 0).
Question 16. If 3x + 2y = 12, what is the value of y when x = 2?
a) 4
b) 3
c) 2
d) 1
Answer:
a) 4 — Substitute x = 2: 3(2) + 2y = 12 → 6 + 2y = 12 → 2y = 6 → y = 4.
Question 17. What is the slope of the line given by the equation 2x – 3y = 6?
a) 2/3
b) -2/3
c) 3/2
d) -3/2
Answer:
b) -2/3 — Rewrite the equation in slope-intercept form: y = (2/3)x – 2. The slope is -2/3.
Question 18. Which of the following is not a solution of x + y = 8?
a) (4, 4)
b) (6, 2)
c) (3, 5)
d) (5, 4)
Answer:
d) (5, 4) — Substitute x = 5 and y = 4: 5 + 4 = 9 ≠ 8, so it is not a solution.
Question 19. Which equation represents the total cost of buying x apples at `10 each and y oranges at `15 each?
a) 10x + 15y = 100
b) 10x – 15y = 100
c) 15x + 10y = 100
d) 10x + 15y = Total cost
Answer:
d) 10x + 15y = Total cost — The total cost is represented as the sum of 10 per apple and 15 per orange.
Question 20. Which of the following equations has a slope of -1?
a) x + y = 0
b) x – y = 0
c) y = x
d) 2x + y = 0
Answer:
a) x + y = 0 — Rewrite the equation as y = -x. The slope is the coefficient of x, which is -1.
Question 21. Which of the following equations represents a horizontal line?
a) y = -4
b) x = 2
c) x + y = 4
d) y = x
Answer:
a) y = -4 — An equation of the form y = constant represents a horizontal line.
Question 22. What is the solution of the equation x – y = 2 when x = 5?
a) (5, 3)
b) (5, -3)
c) (5, 7)
d) (5, 2)
Answer:
a) (5, 3) — Substitute x = 5: 5 – y = 2 → y = 3. The solution is (5, 3).
Question 23. What is the y-intercept of the equation 3x – y = 9?
a) (0, 9)
b) (0, -9)
c) (9, 0)
d) (-9, 0)
Answer:
b) (0, -9) — Substitute x = 0: 3(0) – y = 9 → -y = 9 → y = -9. The y-intercept is (0, -9).
Question 24. Which of the following is true about the equation 4x + 6y = 12?
a) It has one solution.
b) It has no solution.
c) It has infinitely many solutions.
d) It has exactly two solutions.
Answer:
c) It has infinitely many solutions — A linear equation in two variables always has infinitely many solutions.
Question 25. If the cost of a notebook is `x and the cost of a pen is `y, which equation represents the total cost of 3 notebooks and 5 pens being `50?
a) 3x + 5y = 50
b) 3x – 5y = 50
c) 5x + 3y = 50
d) x + y = 50
Answer:
a) 3x + 5y = 50 — The equation represents the total cost of 3 notebooks and 5 pens.
Question 26. What is the slope of the line represented by 5x + y = 10?
a) -5
b) 5
c) -1/5
d) 1/5
Answer:
c) -1/5 — Rewrite as y = -5x + 10. The slope is the coefficient of x, which is -1/5.
Question 27. What is the solution of 2x + y = 10 when y = 4?
a) (3, 4)
b) (5, 4)
c) (4, 4)
d) (2, 4)
Answer:
b) (5, 4) — Substitute y = 4: 2x + 4 = 10 → 2x = 6 → x = 5. The solution is (5, 4).
Question 28. Which of the following equations is equivalent to x + y = 5?
a) 2x + 2y = 10
b) x – y = 5
c) x + y = 10
d) 2x + y = 5
Answer:
a) 2x + 2y = 10 — Dividing the equation 2x + 2y = 10 by 2 gives x + y = 5, which is equivalent.
Question 29. Which of the following is a solution of 3x – 2y = 6?
a) (4, 3)
b) (2, 0)
c) (0, 3)
d) (6, 0)
Answer:
b) (2, 0) — Substitute x = 2 and y = 0: 3(2) – 2(0) = 6. The solution is (2, 0).
Question 30. Which of the following represents the equation of a line passing through the origin?
a) x + y = 0
b) x – y = 1
c) y = 2x + 1
d) x = 1
Answer:
a) x + y = 0 — The line passes through the origin, as it satisfies the condition (0, 0).
Question 31. What is the slope of the line represented by y = -2x + 3?
a) 2
b) -2
c) 3
d) -3
Answer:
b) -2 — In the slope-intercept form y = mx + c, the slope is the coefficient of x, which is -2.
Question 32. What is the solution of x + 2y = 8 if x = 4?
a) (4, 4)
b) (4, 2)
c) (4, -2)
d) (4, 0)
Answer:
b) (4, 2) — Substitute x = 4: 4 + 2y = 8 → 2y = 4 → y = 2. The solution is (4, 2).
