A construction company needs to transport a mix of small and large building materials to a job site. Each small container can hold 30 materials, and each large container can hold 50 materials. A total of 10 containers were sent, which can hold 400 materials altogether. Solve the system of equations to find the number of small and large containers sent.
1. 30x + 50y = 400
2. x + y = 10
To solve this system of equations, we can use the substitution method. First, solve equation 2 for x:
x = 10 - y
Next, substitute this expression for x into equation 1:
30(10 - y) + 50y = 400
300 - 30y + 50y = 400
20y = 100
y = 5
Now, we can substitute y = 5 back into equation 2 to solve for x:
x + 5 = 10
x = 5
Therefore, the construction company sent 5 small containers and 5 large containers to transport the building materials.