To determine which of the given ordered pairs is a solution to the system of equations provided by Tina, we need to substitute each pair into both equations and check if they satisfy both.
The equations are:
- \(3x - y = 9\)
- \(4x + y = 5\)
We will test each of the given points:
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For (–3, 2):
- Equation 1: \(3(-3) - 2 = -9 - 2 = -11 \quad (\text{not } 9)\)
- Equation 2: \(4(-3) + 2 = -12 + 2 = -10 \quad (\text{not } 5)\)
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For (–2, 3):
- Equation 1: \(3(-2) - 3 = -6 - 3 = -9 \quad (\text{not } 9)\)
- Equation 2: \(4(-2) + 3 = -8 + 3 = -5 \quad (\text{not } 5)\)
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For (2, –3):
- Equation 1: \(3(2) - (-3) = 6 + 3 = 9 \quad (\text{yes } 9)\)
- Equation 2: \(4(2) + (-3) = 8 - 3 = 5 \quad (\text{yes } 5)\)
-
For (3, –2):
- Equation 1: \(3(3) - (-2) = 9 + 2 = 11 \quad (\text{not } 9)\)
- Equation 2: \(4(3) + (-2) = 12 - 2 = 10 \quad (\text{not } 5)\)
From the testing, only the point (2, –3) satisfies both equations:
- \(3(2) - (-3) = 9\)
- \(4(2) + (-3) = 5\)
Therefore, Tina can conclude that (2, –3) is a solution to the system of linear equations.