write three linear equations: one with infinite answers, one with no solution, and one with one solution. write a real world solution that goes with at lease one system of equations. show your work
Equation 1 (Infinite Answers): 2x + 4y = 8
This equation has infinite answers because it can be rewritten as y = -0.5x + 2, where there are infinite possible pairs of x and y that satisfy the equation.
Equation 2 (No Solution): 3x + 2y = 10
This equation has no solution because it cannot be rearranged to have the same slope or y-intercept as Equation 1.
Equation 3 (One Solution): 5x - 3y = 7
This equation has one solution because it has a unique slope and y-intercept that does not match the other two equations.
Real World Solution: Let's consider a scenario where a farmer is selling apples and oranges. Each apple is priced at $2 and each orange is priced at $1. The farmer sells a total of 8 fruits for a total of $12. Using a system of equations, we can represent this scenario:
Equation 1: 2x + y = 8 (total fruits)
Equation 2: x + y = 12 (total revenue)
- Equations 1 and 2 will have one unique solution, x = 2 and y = 6.
- Therefore, the farmer sold 2 apples and 6 oranges.
Work:
2x + y = 8
x + y = 12
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x = 2
y = 6