# Algebra 1 : How to find the solution for a system of equations

## Example Questions

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### Example Question #92 : Equations / Solution Sets

A blue train leaves San Francisco at 8AM going 80 miles per hour. At the same time, a green train leaves Los Angeles, 380 miles away, going 60 miles per hour. Assuming that they are headed towards each other, when will they meet, and about how far away will they be from San Francisco?

Around 3AM the next day, about 1,520 miles away from San Francisco

Around 2:45AM, about 200.15 miles away from San Francisco

Around 10:43AM, about 217.12 miles away from San Francisco

The two trains will never meet.

Around 10:43AM, about 217.12 miles away from San Francisco

Explanation:

This system can be solved a variety of ways, including graphing. To solve algebraically, write an equation for each of the different trains. We will use y to represent the distance from San Francisco, and x to represent the time since 8AM.

The blue train travels 80 miles per hour, so it adds 80 to the distance from San Francisco every hour. Algebraically, this can be written as .

The green train starts 380 miles away from San Francisco and subtracts distance every hour. This equation should be .

To figure out where these trains' paths will intersect, we can set both right sides equal to each other, since the left side of each is .