Now try writing and solving your own systems of linear equations, one with infinite solutions, one with no solution, and one with one solution write a real world scenario that goes with at least one system of equations show your work
Real-world scenario: A bakery sells both cookies and muffins. On Monday, they sold a total of 50 items and made $200. Cookies cost $2 each and muffins cost $3 each.
1) Infinite solutions:
Let x be the number of cookies sold and y be the number of muffins sold.
x + y = 50
2x + 3y = 200
To find infinite solutions, let's multiply the first equation by 2 and subtract it from the second equation:
2x + 2y = 100
2x + 3y = 200
y = 100
Since y = 100, there are infinite solutions to this system of equations because there are infinite combinations of cookies and muffins that can be sold to make $200.
2) No solution:
Let x be the number of cookies sold and y be the number of muffins sold.
x + y = 50
3x + 3y = 175
To find no solution, let's simplify the second equation:
x + y = 50
x + y = 58.33
Since the second equation contradicts the first equation, there are no solutions to this system of equations.
3) One solution:
Let x be the number of cookies sold and y be the number of muffins sold.
x + y = 50
2x + 3y = 175
To find one solution, let's multiply the first equation by 2 and subtract it from the second equation:
2x + 2y = 100
2x + 3y = 175
y = 75
Substitute y = 75 into the first equation:
x + 75 = 50
x = -25
The solution is x = -25 (which doesn't make sense in this scenario) and y = 75. The bakery sold 75 muffins and -25 cookies, which is not possible.