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Question (11)

QN0036581

If the solution of 3x + 2y = 13 and x - y = 1 is (x, y), then x + y equals:

(A) 4
(B) 5
(C) 6
(D) 7

Correct Answer: B

Explanation:

x = y + 1. Therefore, 3(y + 1) + 2y = 13, giving y = 2 and x = 3. Hence x + y = 5.

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Question (12)

QN0036582

The equations x + 2y = 5 and 2x + 4y = 10 have:

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

Correct Answer: C

Explanation:

The second equation is twice the first, so the lines coincide.

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Question (13)

QN0036583

For the pair 5x + 2y = 9 and 10x + 4y = 15, the lines are:

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

Correct Answer: C

Explanation:

5/10 = 2/4, but 9/15 ≠ 1/2. Hence the lines are parallel.

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Question (14)

QN0036584

A pair of linear equations having infinitely many solutions is called:

(A) Inconsistent pair
(B) Independent pair
(C) Dependent pair
(D) Unique pair

Correct Answer: C

Explanation:

Coincident lines have infinitely many common points and form a dependent pair.

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Question (15)

QN0036585

Which method is particularly useful when one equation can easily be rearranged to express one variable in terms of the other?

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

Correct Answer: B

Explanation:

In substitution, one variable is expressed in terms of the other and substituted into the second equation.

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Question (16)

QN0036586

Solve x + y = 9 and x - y = 3. The value of xy is:

(A) 15
(B) 18
(C) 20
(D) 24

Correct Answer: B

Explanation:

Adding gives 2x = 12, so x = 6 and y = 3. Therefore, xy = 18.

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Question (17)

QN0036587

The equations 3x + 4y = 11 and 6x + 8y = 22 have:

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

Correct Answer: C

Explanation:

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

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Question (18)

QN0036588

If 2x + 5y = 19 and x + y = 5, then y is:

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

Correct Answer: B

Explanation:

x = 5 - y. Substitution gives 2(5 - y) + 5y = 19, so y = 3.

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Question (19)

QN0036589

The pair 7x - 3y = 8 and 14x - 6y = 20 represents:

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

Correct Answer: C

Explanation:

7/14 = (-3)/(-6) = 1/2, but 8/20 ≠ 1/2. Hence the lines are parallel.

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Question (20)

QN0036590

If x = 2, y = 3 is the solution of ax + y = 7, then a equals:

(A) 1
(B) 2
(C) 3
(D) 4

Correct Answer: B

Explanation:

Substituting x = 2 and y = 3 gives 2a + 3 = 7, so a = 2.

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Question (11)

If the solution of 3x + 2y = 13 and x - y = 1 is (x, y), then x + y equals:

Explanation:

Link:

Question (12)

The equations x + 2y = 5 and 2x + 4y = 10 have:

Explanation:

Link:

Question (13)

For the pair 5x + 2y = 9 and 10x + 4y = 15, the lines are:

Explanation:

Link:

Question (14)

A pair of linear equations having infinitely many solutions is called:

Explanation:

Link:

Question (15)

Which method is particularly useful when one equation can easily be rearranged to express one variable in terms of the other?

Explanation:

Link:

Question (16)

Solve x + y = 9 and x - y = 3. The value of xy is:

Explanation:

Link:

Question (17)

The equations 3x + 4y = 11 and 6x + 8y = 22 have:

Explanation:

Link:

Question (18)

If 2x + 5y = 19 and x + y = 5, then y is:

Explanation:

Link:

Question (19)

The pair 7x - 3y = 8 and 14x - 6y = 20 represents:

Explanation:

Link:

Question (20)

If x = 2, y = 3 is the solution of ax + y = 7, then a equals:

Explanation:

Link:

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