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 Clarence's house that he runs regularly, a short loop and a long loop. Last week, he ran short loops and long loops, for a total of miles. This week, he ran short loops and long loops, covering a total of miles. What is the length of each loop?The short loop has a length of miles, and the long loop has a length of miles.
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 Clarence's house that he runs regularly, a short loop and a long loop. Last week, he ran short loops and long loops, for a total of miles. This week, he ran short loops and long loops, covering a total of miles. What is the length of each loop?The short loop has a length of miles, and the long loop has a length of miles.
- Define variables: Define the variables for the lengths of the short and long loops.Let be the length of the short loop and be the length of the long loop.
- Write equations: Write the system of equations based on the given information.First week: short loops and long loops equal miles.Second week: short loops and long loops equal miles.This gives us the system of equations:
- Eliminate variable: Decide which variable to eliminate.We can eliminate by subtracting the second equation from the first because the coefficients of are the same in both equations.
- Subtract equations: Subtract the second equation from the first to eliminate . - = - \)We have found the length of the short loop.
- Substitute values: Substitute the value of into one of the original equations to solve for . Using the second equation: We have found the length of the long loop.
