Question

1. reasoning the system of equations below shows the distance in miles, y, two trains travel in time, x. what conclusion can you make about the system of equations? interpret your result in the context of the problem.

train a: y = 1.6x + 4
train b: 7y = 11.2x + 28

Explanation:

Step1: Simplify Train B's equation

Divide \(7y = 11.2x+28\) by \(7\). We get \(y=\frac{11.2x + 28}{7}=1.6x + 4\)

Step2: Analyze the system of equations

The system of equations is \(y = 1.6x+4\) (Train A) and \(y=1.6x + 4\) (after simplifying Train B's equation). Since the two equations are identical.

Answer:

The system of equations has infinitely many solutions. In the context of the problem, it means that the two trains are always at the same distance from the starting - point at the same time. So, the two trains are always in the same position relative to the starting point as time \(x\) progresses.