Question

Examine the system below:

y = 3x - 1 and y = -(2/5)x - 1. Which conclusion is true about the system of equations?

a. The system has no solution.
b. The system has a unique solution.
c. The system has infinitely many solutions.
d. The conclusion cannot be determined from the given information.

Answer 1

The system of equations y = 3x - 1 and y = -(2/5)x - 1 has a unique solution.

Step-by-step explanation:

The given system of equations is y = 3x - 1 and y = -(2/5)x - 1.

To determine which conclusion is true about the system, we need to compare the slopes and y-intercepts of the two equations.

• Slope of the first equation (3) is not equal to the slope of the second equation (-2/5), so the lines are not parallel.
• Y-intercept of the first equation (-1) is not equal to the y-intercept of the second equation (-1), so the lines do not intersect at the same point.

Since the lines are neither parallel nor intersect at the same point, the system of equations has a unique solution. Therefore, the correct conclusion is option b. The system has a unique solution.