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:
- 9x - 2y = -9
- 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.