Question

Write three linear equations one with infinite solutions one with no Solutions and one with one solution write a World scenario that goes with at least one of the systems of equations show your work

Answer 1

Can you shorten it

Answer 2

1) Infinite solutions:
x + y = 5
2x + 2y = 10 (equivalent to x + y = 5)

This system has infinite solutions because the second equation is just a multiple of the first equation. Every point on the line x + y = 5 will satisfy both equations.

2) No solutions:
x + 2y = 5
2x + 4y = 8

This system has no solution because the second equation is not a multiple of the first equation. The two lines are parallel and will never intersect.

3) One solution:
2x + y = 7
4x + 2y = 14

Let's create a world scenario for the system with one solution:

Suppose a farmer is considering planting two types of crops, corn and wheat. Each acre of corn requires 2 workers and 1 bag of fertilizer, while each acre of wheat requires 4 workers and 2 bags of fertilizer. The farmer has a total of 7 workers and 14 bags of fertilizer available.

Let x represent the number of acres of corn planted and y represent the number of acres of wheat planted. The system of equations would be:

2x + y = 7 (equation 1: total workers)
4x + 2y = 14 (equation 2: total bags of fertilizer)

Solving this system, we get x = 3, y = 1. Therefore, the farmer should plant 3 acres of corn and 1 acre of wheat to utilize all available resources effectively.

Answer 3

Sure!

World scenario: A farmer needs to decide how many acres of corn and wheat to plant. Each acre of corn requires 2 workers and 1 bag of fertilizer, while each acre of wheat requires 4 workers and 2 bags of fertilizer. The farmer has 7 workers and 14 bags of fertilizer available.

Equations:
2x + y = 7 (total workers)
4x + 2y = 14 (total bags of fertilizer)

Solution:
x = 3, y = 1
The farmer should plant 3 acres of corn and 1 acre of wheat to use all resources efficiently.