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Worksheet
Directions: Use this worksheet to record your answers to the questions about linear equations. When you are finished, save this worksheet with your answers and submit it for a portfolio grade.
Investigate and explain the different number of solutions an equation can have.
Question 1
Examine the six different equations that follow. Determine which equations have one solution, no solution, or infinitely many solutions.
- Put a circle around the two equations that have infinite solutions.
- Put a square around the two equations that have no solution.
- Underline the two equations that have one solution.
Question 2: Infinite Solutions
Consider the two equations you circled, which form a system with infinite solutions.
- Solve the equations.
- What do you notice about these equations?
- What does it mean to have infinite solutions?
Plug in \( x = 3 \) and \( x = -2 \) for both of the original equations to show that the equations can have more than one solution.
- Solve the equations.
- Explain your work.
Question 3: No Solutions
Consider the two equations you put a square around, which form a system with no solution.
- Solve the equations.
- What do you notice about these equations?
- What does it mean to have no solutions?
Plug in \( x = 2 \) and \( x = -3 \) for both of the original equations to show that the equations will have no solutions.
- Explain your work.
Question 4: One Solution
Consider the two equations that you underlined, which form a system with one solution.
- Solve the equations.
- What do you notice about these equations?
- What does it mean to have one solution?
Use your answers to your original equations. Plug them into their own equations to show their solutions are true. Use \( x = 4 \) into each original equation to prove they are false solutions.
- Explain your work.
Question 5: Writing Linear Equations
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.
Feel free to modify any part of it as needed!
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