Question

Which system of equations below has exactly one solution?

A. (y=-8x-6) and (y=-8x+6)
B. (y=-8x-6) and (frac{1}{2}y=-4x-3)
C. (y=-8x-6) and (y=8x-6)
D. (y=-8x-6) and (-y=8x+6)

Answer 1

Option (C) y = -8x - 6 and y = 8x - 6 is the correct answer because the two equations have different slopes, indicating that the lines will intersect at exactly one point.

Step-by-step explanation:

To determine which system of equations has exactly one solution, we should look for a pair of equations that represent two lines that intersect at exactly one point. This happens when the lines have different slopes.

• (A) y = -8x - 6 and y = -8x + 6 are parallel lines because they have the same slope (-8) but different y-intercepts, so they will never intersect (no solution).
• (B) y = -8x - 6 and 1/2y = -4x - 3 are equivalent when the second equation is multiplied by 2 throughout (no solution).
• (C) y = -8x - 6 and y = 8x - 6 have different slopes and therefore will intersect at exactly one point (one solution).
• (D) y = -8x - 6 and -y = 8x + 6 are also equivalent when the second equation is multiplied by -1 throughout (no solution).

The correct answer is (C) y = -8x - 6 and y = 8x - 6 because the lines intersect at exactly one point, since they have different slopes.