Question

Which system has exactly one solution?

a) 3x - y = 8, 6x - 2y = 16
A) 3x - y = 8, 6x - 2y = 16
B) y = 4x + 9, y = 4x - 9
C) -6x + y = 2, y = 6x + 2
D) 3x + 2y = 4, x - y = 3

b) y = 4x + 9, y = 4x - 9
A) 3x - y = 8, 6x - 2y = 16
B) y = 4x + 9, y = 4x - 9
C) -6x + y = 2, y = 6x + 2
D) 3x + 2y = 4, x - y = 3

c) -6x + y = 2, y = 6x + 2
A) 3x - y = 8, 6x - 2y = 16
B) y = 4x + 9, y = 4x - 9
C) -6x + y = 2, y = 6x + 2
D) 3x + 2y = 4, x - y = 3

d) 3x + 2y = 4, x - y = 3
A) 3x - y = 8, 6x - 2y = 16
B) y = 4x + 9, y = 4x - 9
C) -6x + y = 2, y = 6x + 2
D) 3x + 2y = 4, x - y = 3

Answer 1

The system that has exactly one solution is option B) y = 4x + 9, y = 4x - 9.

Step-by-step explanation:

The system that has exactly one solution is option B) y = 4x + 9, y = 4x - 9.

A system of equations has exactly one solution when the two lines represented by the equations intersect at a single point. In this case, the equations y = 4x + 9 and y = 4x - 9 represent two lines with different slopes and different y-intercepts. Therefore, they will intersect at a single point, giving us one solution.

Answer 2

The system that has exactly one solution is B) y = 4x + 9, y = 4x - 9.

Step-by-step explanation:

One Solution Criteria: A system of linear equations has exactly one solution when the lines represented by the equations intersect at a single point.

Analysis of Options:

Option A: The equations in option A are dependent, representing the same line. This results in infinitely many solutions.

Option B: The two lines in option B have different slopes, ensuring they intersect at a unique point. This system has one solution.

Option C: The lines in option C are parallel, indicating no intersection and no solution.

Option D: The lines in option D intersect at a unique point, resulting in one solution.

Option B is the answer.