One solution:
4x+22=8x+10
5x+5=5x+4
No solution:
2x+3+2x+7
7x+3+7x+3
Infinite solutions:
3x+18=5x+8
3(4x+8)=4(3x+6)
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 cookies and muffins. Each cookie costs $1.50 and each muffin costs $2.00. On a certain day, the bakery sold a total of 30 items and made $45. Write and solve a system of equations to find out how many cookies and muffins were sold.
Let x be the number of cookies sold and y be the number of muffins sold.
1.50x + 2.00y = 45
x + y = 30
1.50x + 2.00y = 45
2(1.50x + 2.00y) = 2(45)
3x + 4y = 90
x + y = 30
-3x - 4y = -90
3x + 4y = 90
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0 = 0
Since the two equations are the same, the system has infinite solutions. This means that the bakery could have sold any combination of cookies and muffins that adds up to 30 items and $45 in revenue.