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Question (1)

QN0036571

Which of the following represents a pair of linear equations in two variables?

(A) x² + y = 5, x + y = 3
(B) 2x + 3y = 7, 4x - y = 5
(C) xy = 6, x + y = 5
(D) x² + y² = 9, x - y = 2

Correct Answer: B

Explanation:

A linear equation has variables only to the first degree and no product of variables.

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Question (2)

QN0036572

If two lines intersect at exactly one point, the corresponding pair of linear equations has:

(A) No solution
(B) Exactly one solution
(C) Infinitely many solutions
(D) Two solutions

Correct Answer: B

Explanation:

The coordinates of the intersection point give the unique solution.

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Question (3)

QN0036573

The pair of equations 2x + 3y = 6 and 4x + 6y = 12 represents:

(A) Intersecting lines
(B) Parallel lines
(C) Coincident lines
(D) Perpendicular lines

Correct Answer: C

Explanation:

The second equation is twice the first, so both equations represent the same line.

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Question (4)

QN0036574

If two lines are parallel, the pair of linear equations is:

(A) Consistent
(B) Dependent
(C) Inconsistent
(D) Identical

Correct Answer: C

Explanation:

Parallel distinct lines have no common point, hence no solution.

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Question (5)

QN0036575

For the equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the condition for intersecting lines is:

(A) a₁/a₂ = b₁/b₂
(B) a₁/a₂ ≠ b₁/b₂
(C) a₁/a₂ = c₁/c₂
(D) b₁/b₂ = c₁/c₂

Correct Answer: B

Explanation:

Unequal ratios of the coefficients of x and y indicate intersecting lines.

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Question (6)

QN0036576

The equations 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 have:

(A) One solution
(B) No solution
(C) Infinitely many solutions
(D) Exactly two solutions

Correct Answer: C

Explanation:

All three coefficient ratios are equal: 3/6 = (-2)/(-4) = 5/10.

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Question (7)

QN0036577

The equations 4x + 6y - 8 = 0 and 2x + 3y + 5 = 0 represent:

(A) Coincident lines
(B) Intersecting lines
(C) Parallel lines
(D) The same equation

Correct Answer: C

Explanation:

4/2 = 6/3 = 2, but -8/5 ≠ 2. Therefore, the lines are parallel.

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Question (8)

QN0036578

Which algebraic method directly removes one variable by making its coefficients equal?

(A) Graphical method
(B) Substitution method
(C) Elimination method
(D) Factorisation method

Correct Answer: C

Explanation:

In the elimination method, equations are multiplied by suitable constants and then added or subtracted to eliminate a variable.

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Question (9)

QN0036579

The pair x + y = 7 and x - y = 1 has solution:

(A) (3, 4)
(B) (4, 3)
(C) (5, 2)
(D) (2, 5)

Correct Answer: B

Explanation:

Adding the equations gives 2x = 8, so x = 4 and y = 3.

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Question (10)

QN0036580

The pair 2x + 3y = 12 and 4x + 6y = 24 is:

(A) Inconsistent
(B) Consistent with a unique solution
(C) Dependent and consistent
(D) Neither consistent nor inconsistent

Correct Answer: C

Explanation:

The second equation is twice the first, so infinitely many solutions exist.

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Question (1)

Which of the following represents a pair of linear equations in two variables?

Explanation:

Link:

Question (2)

If two lines intersect at exactly one point, the corresponding pair of linear equations has:

Explanation:

Link:

Question (3)

The pair of equations 2x + 3y = 6 and 4x + 6y = 12 represents:

Explanation:

Link:

Question (4)

If two lines are parallel, the pair of linear equations is:

Explanation:

Link:

Question (5)

For the equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, the condition for intersecting lines is:

Explanation:

Link:

Question (6)

The equations 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 have:

Explanation:

Link:

Question (7)

The equations 4x + 6y - 8 = 0 and 2x + 3y + 5 = 0 represent:

Explanation:

Link:

Question (8)

Which algebraic method directly removes one variable by making its coefficients equal?

Explanation:

Link:

Question (9)

The pair x + y = 7 and x - y = 1 has solution:

Explanation:

Link:

Question (10)

The pair 2x + 3y = 12 and 4x + 6y = 24 is:

Explanation:

Link:

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