Writing Systems of Equations

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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.

(1). Choose two equations that make up the system represented by the graph.

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