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** Write Systems of Equations.**

- Move the blue and red sliders below to form two lines of your own choosing.
- After you choose the two lines you’ll be working with, solve the system of linear equations that they form.
- Write down the system of equations and its answer.
- Compare the answer with point A.
- Do the same thing with different lines.

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**Match a System of Equations with the Number of Solutions.**

Match each system of equations with the number of solutions the system has.

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**Solve a System of Equations.**

Here are a lot of systems of equations.

(1). Without solving, identify 3 systems that you think would be the **least difficult **for you to solve. Explain your reasoning.

(2). Without solving, identify 3 systems you think would be the **most difficult **for you to solve. Explain your reasoning.

(3). Choose 4 systems to solve. At least one should be from your “least difficult” list and one should be from your “most difficult” list.

(a). 1st system with solution: (least difficult.)

(b). 2nd system with solution:

(c). 3rd system with solution:

(d). 4th system with solution: (most difficult.)

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Decide which story can be represented by the system of equations = + 6 and + = 100.

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Clare and Noah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points.

(1). Write a system of equations that describes Clare and Noah’s outcomes. Use to represent the number of points for a goal and to represent the number of points for a penalty.

(2). Solve the system. What does your solution mean?

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Estimate the coordinates of the point where the two lines meet.

(2). Solve the system of equations and confirm the accuracy of your estimate.

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