Unfortunately, as an AI language model, I cannot read or access any external files or worksheets. However, I can provide you with guidance on how to approach each question in the portfolio.
Question 1: Examine the six different equations and determine which have one solution, no solution, and infinite solutions. Put a circle around equations with infinite solutions, put a square around equations with no solution, and underline equations with one solution.
To determine the type of solution for each equation, you need to solve the equations using appropriate methods like substitution or elimination. For equations with infinite solutions, there will be a relationship between the equations, and for equations with no solution, you will reach a contradiction. Equations with one solution will have a unique solution for both variables.
Question 2: Solve the two equations that form a system with infinite solutions. Notice any patterns or relationships between the equations, and explain what it means to have infinite solutions. Plug in more than one point into the original equations to demonstrate that there can be more than one solution.
When solving the equations with infinite solutions, you should end up with the same equation on both sides of the equation. This means that any value of the variables that satisfies one equation will also satisfy the other equation. By plugging in different values for the variables, you can demonstrate that there are infinitely many solutions.
Question 3: Solve the two equations that form a system with no solution. Notice any patterns or relationships between the equations, and explain what it means to have no solution. Plug in a few points into the original equations to demonstrate that they can have no solution.
When solving the equations with no solution, you will reach a contradiction or an inconsistent statement when simplifying the equations. This means that there is no combination of values for the variables that will satisfy both equations simultaneously. By plugging in various points, you can demonstrate that the equations are not satisfied by any particular combination of values.
Question 4: Solve the two equations that form a system with one solution. Notice any patterns or relationships between the equations, and explain what it means to have one solution. Plug in a few points into the original equations to demonstrate that the system has one solution.
When solving the equations with one solution, you will obtain a unique and specific solution for both variables. The equations will intersect at a single point on a graph, representing the solution to the system. By plugging in different points, you can demonstrate that the equations only satisfy a particular combination of values.
Question 5: Write and solve your own systems of linear equations. Create one with infinite solutions, one with no solution, and one with one solution. Provide a real-world scenario to explain the system of equations.
For each scenario, you will need to define the variables, write down the equations based on the given information, and solve the system using appropriate methods. Make sure to demonstrate the type of solution for each system (infinite solutions, no solution, or one solution) and explain how it relates to the real-world scenario you provided.
Remember to refer to the provided rubric to check your work and ensure you have addressed all the requirements for the portfolio.
Solving Linear Equations Portfolio
Use the worksheet to record your answers to the Solving Linear Equations portfolio activity. When you are finished, save your worksheet with your answers and submit it for a portfolio grade.
Investigate and explain the different types of solutions to a system of equations.
Question 1
Examine the six different equations that follow. Determine which pairs of equations have one solution, no solution, and infinite solutions. On your worksheet,
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.
2x+37x+34x+225x+53x+183(4x+8)======2x+77x+38x+105x+45x+84(3x+6)
What do you notice about equations that are in each of these categories? Use complete sentences to answer the questions that follow.
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 more than one point into the original equations and check to show that the equations can have more than one solution. 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 solution? Plug a few points into the original equations and check to show that they can have no solution. 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? Plug a few points into the original equations and check to show that the system of equations has one solution. 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.
Solving Linear Equations Portfolio Worksheet
Use the rubric to check your work on the portfolio.
Solving Linear Equations Portfolio Rubric
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