Question

Rajiv wrote the equations y=8x−2 and y=−4x−5. What can Rajib conclude about the solution to this system of equations?

A) No solution; the lines are parallel.
B) Infinitely many solutions; the lines are coincident.
C) One solution; the lines intersect at a single point.
D) Two solutions; the lines intersect at two distinct points.

Answer 1

The lines represented by the equations y = 8x - 2 and y = -4x - 5 have different slopes and hence intersect at one point, indicating that there is one solution to this system of equations.

Step-by-step explanation:

Rajiv analyzed two linear equations: y = 8x - 2 and y = -4x - 5. To determine the relationship between these lines, we need to compare their slopes. The slope of the first line is 8, and the slope of the second line is -4. Since the slopes are different, we can conclude that the lines are not parallel and will intersect at a single point. Therefore, the system of equations has exactly one solution where these two lines meet. This corresponds to option C) One solution; the lines intersect at a single point.