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Question (41)

QN0036611

For what value of k will 2x + 3y = 5 and 4x + 6y = k have infinitely many solutions?

(A) 5
(B) 8
(C) 10
(D) 12

Correct Answer: C

Explanation:

For coincident lines, the second equation must be twice the first. Therefore k = 10.

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Question (42)

QN0036612

For what value of k will 3x + 2y = 7 and 6x + 4y = k be coincident?

(A) 7
(B) 10
(C) 14
(D) 21

Correct Answer: C

Explanation:

The second equation must be exactly twice the first. Therefore k = 14.

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Question (43)

QN0036613

The equations ax + 3y = 6 and 2x + 6y = 12 are coincident. The value of a is:

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

Correct Answer: B

Explanation:

The second equation is twice the first, so a = 2.

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Question (44)

QN0036614

The pair 4x + 3y = 12 and 8x + 6y = 25 has:

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

Correct Answer: C

Explanation:

4/8 = 3/6 = 1/2, but 12/25 ≠ 1/2. Hence the lines are parallel and there is no solution.

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Question (45)

QN0036615

If x = 3, y = 2 satisfies kx + 4y = 17, then k is:

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

Correct Answer: B

Explanation:

Substituting x = 3 and y = 2 gives 3k + 8 = 17, so k = 3.

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Question (46)

QN0036616

The solution of 2x + y = 7 and x + 2y = 8 is:

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

Correct Answer: A

Explanation:

From 2x + y = 7, y = 7 - 2x. Substituting in x + 2y = 8 gives x = 2 and y = 3.

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Question (47)

QN0036617

If two equations have a common solution (4, -1), which equation must be satisfied?

(A) x + y = 2
(B) 2x + y = 7
(C) x - 2y = 5
(D) 3x + y = 10

Correct Answer: B

Explanation:

Substituting (4, -1) in 2x + y gives 2(4) - 1 = 7, so the equation is satisfied.

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Question (48)

QN0036618

A pair of lines is represented by x - 2y + 3 = 0 and 2x - 4y + 6 = 0. If a point (p, q) lies on the first line, then it:

(A) Cannot lie on the second line
(B) Must lie on the second line
(C) Lies only when p = q
(D) Lies only when p = 0

Correct Answer: B

Explanation:

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

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Question (49)

QN0036619

The equations x + y = 10 and 2x - y = 5 intersect at:

(A) (3, 7)
(B) (5, 5)
(C) (6, 4)
(D) (4, 6)

Correct Answer: B

Explanation:

Adding the equations gives 3x = 15, so x = 5. Therefore y = 5.

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Question (50)

QN0036620

Which statement correctly describes a pair of coincident lines?

(A) They have exactly one common point.
(B) They have no common point.
(C) Every point on one line is also on the other line.
(D) They intersect only on the x-axis.

Correct Answer: C

Explanation:

Coincident lines are the same line, so they have infinitely many common points.

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Question (41)

For what value of k will 2x + 3y = 5 and 4x + 6y = k have infinitely many solutions?

Explanation:

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Question (42)

For what value of k will 3x + 2y = 7 and 6x + 4y = k be coincident?

Explanation:

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Question (43)

The equations ax + 3y = 6 and 2x + 6y = 12 are coincident. The value of a is:

Explanation:

Link:

Question (44)

The pair 4x + 3y = 12 and 8x + 6y = 25 has:

Explanation:

Link:

Question (45)

If x = 3, y = 2 satisfies kx + 4y = 17, then k is:

Explanation:

Link:

Question (46)

The solution of 2x + y = 7 and x + 2y = 8 is:

Explanation:

Link:

Question (47)

If two equations have a common solution (4, -1), which equation must be satisfied?

Explanation:

Link:

Question (48)

A pair of lines is represented by x - 2y + 3 = 0 and 2x - 4y + 6 = 0. If a point (p, q) lies on the first line, then it:

Explanation:

Link:

Question (49)

The equations x + y = 10 and 2x - y = 5 intersect at:

Explanation:

Link:

Question (50)

Which statement correctly describes a pair of coincident lines?

Explanation:

Link:

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