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For each ordered pair, determine whether it is a solution to the system of equations.

9x - 2y = -9
7x + 5y = -7
a) (1,13)
b) (0,4)
c) (-6,-5)
d) (2,-7)

User Crankshaft
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1 Answer

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Final answer:

After evaluating each ordered pair by plugging their values into the given system of equations, it was determined that none of the pairs (1,13), (0,4), (-6,-5), or (2,-7) are solutions to both equations.

Step-by-step explanation:

To determine whether each ordered pair is a solution to the system of equations:

  1. 9x - 2y = -9
  2. 7x + 5y = -7

We plug in the x and y values from each pair into both equations to see if both equations are true.

  • a) (1,13): Plugging x=1 and y=13 into both equations:
  • 9(1) - 2(13) = -9, which simplifies to 9 - 26 = -9, which is not true.
  • 7(1) + 5(13) = -7, which simplifies to 7 + 65 = -7, which is also not true.
  • So, (1,13) is not a solution.
  • b) (0,4): Plugging x=0 and y=4 into both equations:
  • 9(0) - 2(4) = -9, which simplifies to -8 = -9, which is not true.
  • 7(0) + 5(4) = -7, which simplifies to 20 = -7, which is also not true.
  • So, (0,4) is not a solution.
  • c) (-6,-5): Plugging x=-6 and y=-5 into both equations:
  • 9(-6) - 2(-5) = -9, which simplifies to -54 + 10 = -9, which is true.
  • 7(-6) + 5(-5) = -7, which simplifies to -42 - 25 = -7, which is not true.
  • So, (-6,-5) is not a solution.
  • d) (2,-7): Plugging x=2 and y=-7 into both equations:
  • 9(2) - 2(-7) = -9, which simplifies to 18 + 14 = -9, which is not true.
  • 7(2) + 5(-7) = -7, which simplifies to 14 - 35 = -7, which is not true.
  • So, (2,-7) is not a solution.

After testing all pairs, we determine that none of the given ordered pairs is a solution to the system of equations.

User Prasanth
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