Ch-4: Linear Equations in Two Variables30 Questions
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1. What is the general standard form of a linear equation in two variables?
A. ax + b = 0
B. ax + by + c = 0
C. ax² + by + c = 0
D. ax + by² + c = 0
Answer: B. ax + by + c = 0
Explanation: The general form of a linear equation in two variables x and y is ax + by + c = 0, where a, b, and c are real numbers and a, b are not both zero.
2. How many solutions does a linear equation in two variables have?
A. Unique solution
B. Exactly two solutions
C. Infinitely many solutions
D. No solution
Answer: C. Infinitely many solutions
Explanation: Every linear equation in two variables represents a straight line on a graph, and every point on that line is a solution, making the number of solutions infinitely many.
3. Express the equation 2x + 3y = 4.37 in the form ax + by + c = 0 and state the values of a, b, and c.
A. a = 2, b = 3, c = 4.37
B. a = 2, b = 3, c = -4.37
C. a = 2, b = -3, c = -4.37
D. a = -2, b = 3, c = 4.37
Answer: B. a = 2, b = 3, c = -4.37
Explanation: Rewriting 2x + 3y = 4.37 as 2x + 3y - 4.37 = 0 gives a = 2, b = 3, and c = -4.37.
4. The graph of a linear equation in two variables is always a:
A. Circle
B. Parabola
C. Straight line
D. Curved line
Answer: C. Straight line
Explanation: A degree-1 polynomial equation in two variables plots as a straight line on the Cartesian plane.
5. 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
Explanation: Substitute x = 2 and y = 0 into 2x + 3y = k ⇒ 2(2) + 3(0) = k ⇒ k = 4.
6. The equation of the x-axis is written as:
A. x = 0
B. y = 0
C. x + y = 0
D. x = y
Answer: B. y = 0
Explanation: On the x-axis, the ordinate (y-coordinate) of every point is always zero. Thus, its equation is y = 0.
7. The equation of the y-axis is represented by:
A. x = 0
B. y = 0
C. x = a
D. y = b
Answer: A. x = 0
Explanation: On the y-axis, the abscissa (x-coordinate) of every point is always zero, so its equation is x = 0.
8. Any line parallel to the y-axis is of the form:
A. y = a
B. x = a
C. x + y = a
D. y = x
Answer: B. x = a
Explanation: A vertical line parallel to the y-axis has a constant x-coordinate 'a' for all points on it.
9. Any line parallel to the x-axis is of the form:
A. x = b
B. y = b
C. x - y = b
D. x + y = 0
Answer: B. y = b
Explanation: A horizontal line parallel to the x-axis has a constant y-coordinate 'b' for all points on it.
10. The point (a, a) always lies on the graph of:
A. x + y = 0
B. y = x
C. x = -y
D. xy = 1
Answer: B. y = x
Explanation: For (a, a), both coordinates are equal, which satisfies the linear equation y = x.
11. Which of the following ordered pairs is a solution of x - 2y = 4?
A. (0, 2)
B. (2, 0)
C. (4, 0)
D. (1, 1)
Answer: C. (4, 0)
Explanation: Substitute (4, 0) into x - 2y: 4 - 2(0) = 4, which equals RHS.
12. If x = 2, y = 1 is a solution of 2x + 3y = k, then k is:
A. 5
B. 6
C. 7
D. 8
Answer: C. 7
Explanation: 2(2) + 3(1) = 4 + 3 = 7 = k.
13. The linear equation 3x + 12 = 0 in two variables can be written as:
A. 3x + 0y + 12 = 0
B. 0x + 3y + 12 = 0
C. 3x + 12y = 0
D. 3x + y + 12 = 0
Answer: A. 3x + 0y + 12 = 0
Explanation: To represent a single-variable equation in two variables x and y, write the missing variable with coefficient 0: 3x + 0.y + 12 = 0.
14. The graph of x = -3 is a straight line:
A. Parallel to x-axis at distance 3 from origin
B. Parallel to y-axis at distance 3 to left of origin
C. Passing through the origin
D. Parallel to y-axis at distance 3 to right of origin
Answer: B. Parallel to y-axis at distance 3 to left of origin
Explanation: x = -3 is a vertical line parallel to the y-axis situated 3 units to the left of the origin.
15. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement (x = notebook cost, y = pen cost).
A. x + 2y = 0
B. x - 2y = 0
C. 2x + y = 0
D. 2x - y = 0
Answer: B. x - 2y = 0
Explanation: Cost of notebook = 2 × (Cost of pen) ⇒ x = 2y ⇒ x - 2y = 0.
16. The graph of the equation y = mx passes through the:
A. x-axis only
B. y-axis only
C. Origin (0,0)
D. Point (1,1) only
Answer: C. Origin (0,0)
Explanation: Substituting x = 0 gives y = m(0) = 0. Therefore, (0, 0) satisfies y = mx, so it passes through the origin.
17. How many linear equations in x and y can be satisfied by x = 1 and y = 2?
A. Only one
B. Only two
C. Only three
D. Infinitely many
Answer: D. Infinitely many
Explanation: Through a given single point (1, 2) in a plane, infinitely many straight lines can be drawn, each representing a linear equation.
18. The point (-2, 2) lies on the graph of which equation?
A. x + y = 0
B. y = 2x
C. x - y = 0
D. 2x + y = 0
Answer: A. x + y = 0
Explanation: Substitute x = -2 and y = 2 into x + y = 0 ⇒ -2 + 2 = 0. LHS = RHS.
19. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
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