Try writing and solving your own systems of liner equations, one with infinite solutions, one with no solutions, and one with one solution write a real world scenario problem that goes with each equation of equations show your work
Equation 1: Infinite Solutions
Real World Scenario:
You are running a lemonade stand with two friends. You all agree to split the profits equally at the end of the day. However, one of your friends leaves early and doesn't contribute any money towards the ingredients. You and your remaining friend have a disagreement over how to split the profits.
Equation:
3x - 2y = 0
x + 2y = 5
Solution:
To solve this system of equations, we can add the two equations together to eliminate y:
(3x - 2y) + (x + 2y) = 0 + 5
4x = 5
x = 5/4
Now we can substitute the value of x back into one of the equations to solve for y:
5/4 + 2y = 5
2y = 15/4
y = 15/8
The solution to this system of equations is x = 5/4 and y = 15/8. Since the equations have the same slope, they will intersect at one point and have one solution.