Section C Section C Checkpoint

Problem 1

  1. Solve the system without graphing.

    {3x+5y=-96x−7y=33\begin {cases} 3x + 5y = \text{-}9\\ 6x - 7y = 33 \end{cases}

  2. To solve, you wrote at least one new equation. Explain why this is allowed when solving a system.
  3. Explain how you could use a graph to check your answer.
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Solution
  1. x=2,y=-3x = 2, y = \text{-}3
  2. Sample response: It is an equivalent equation, so it maintains the solution of the system.
  3. Sample response: Graph the two lines and look for the intersection at (2,-3)(2,\text{-}3).
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Sample Response
  1. x=2,y=-3x = 2, y = \text{-}3
  2. Sample response: It is an equivalent equation, so it maintains the solution of the system.
  3. Sample response: Graph the two lines and look for the intersection at (2,-3)(2,\text{-}3).

Problem 2

In a system of linear equations, the two equations have the same slope. What information do you know about how many solutions the system has? Explain your reasoning.
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Solution
Sample response: There are either 0 or infinitely many solutions. Because the lines have the same slope, they are either parallel (0 solutions) or equivalent equations (infinitely many solutions).
Show Sample Response
Sample Response
Sample response: There are either 0 or infinitely many solutions. Because the lines have the same slope, they are either parallel (0 solutions) or equivalent equations (infinitely many solutions).