AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.There are two trails near Isaiah's house that he runs regularly, a short loop and a long loop. Last week, he ran short loops and long loop, for a total of kilometers. This week, he ran short loops and long loop, covering a total of kilometers. What is the length of each loop?The short loop has a length of _____ kilometers, and the long loop has a length of _____ kilometers.
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.There are two trails near Isaiah's house that he runs regularly, a short loop and a long loop. Last week, he ran short loops and long loop, for a total of kilometers. This week, he ran short loops and long loop, covering a total of kilometers. What is the length of each loop?The short loop has a length of _____ kilometers, and the long loop has a length of _____ kilometers.
- Define variables: Define the variables for the lengths of the short and long loops.Let be the length of the short loop in kilometers.Let be the length of the long loop in kilometers.
- Write equations: Write the system of equations based on the given information.First week: short loops and long loop equal kilometers.Second week: short loops and long loop equal kilometers.This gives us the system of equations:
- Eliminate variable: Decide which variable to eliminate.We can eliminate by subtracting the first equation from the second equation because they both have the same coefficient for .
- Subtract equations: Subtract the first equation from the second equation to eliminate and solve for .
- Substitute value: Substitute the value of into one of the original equations to solve for . Using the first equation:
