write three linear equations: one with infinite answers, one with no solution, and one with one solution using only x as a variable. write a real world solution that goes with at lease one system of equations. show your work
1) Infinite solutions:
x - 2x = 0
This equation simplifies to:
-x = 0
Thus, x can be any real number. Therefore, the solution has infinite solutions.
2) No solution:
2x + 4 = 2x - 3
This equation simplifies to:
4 = -3
This is a contradictory statement, so there is no solution to this equation.
3) One solution:
3x = 12
This equation simplifies to:
x = 4
Therefore, x = 4 is the only solution to this equation.
Real world solution example:
Let's say we have a situation where a company produces and sells t-shirts. The cost to produce each t-shirt is $5, and they sell each t-shirt for $10. The revenue for selling x number of t-shirts can be represented by the equation:
Revenue = 10x
The cost for producing x number of t-shirts can be represented by the equation:
Cost = 5x
To find the breakeven point where the revenue equals the cost, we can set these two equations equal to each other:
10x = 5x
5x = 0
x = 0
Since x = 0 is the only solution, the breakeven point for the company would be selling 0 t-shirts, in which case the revenue would equal the cost.