To determine which of the given points is a solution to the system of equations, we need to substitute the x-coordinate of each point into the equations \( y = 23x - 5 \) and \( y = 73x - 1 \) and see if we get the same y-coordinate from both equations.
Let's test each point:
1. Point \((-2.4, -6.6)\)
- For \( y = 23x - 5 \): \[ y = 23(-2.4) - 5 = -55.2 - 5 = -60.2 \]
- For \( y = 73x - 1 \): \[ y = 73(-2.4) - 1 = -175.2 - 1 = -176.2 \]
- These do not match \( -6.6 \).
2. Point \((2.4, -6.6)\)
- For \( y = 23x - 5 \): \[ y = 23(2.4) - 5 = 55.2 - 5 = 50.2 \]
- For \( y = 73x - 1 \): \[ y = 73(2.4) - 1 = 175.2 - 1 = 174.2 \]
- These do not match \( -6.6 \).
3. Point \((-2.4, 6.6)\)
- For \( y = 23x - 5 \): \[ y = 23(-2.4) - 5 = -55.2 - 5 = -60.2 \]
- For \( y = 73x - 1 \): \[ y = 73(-2.4) - 1 = -175.2 - 1 = -176.2 \]
- These do not match \( 6.6 \).
4. Point \((-1.2, 3.3)\)
- For \( y = 23x - 5 \): \[ y = 23(-1.2) - 5 = -27.6 - 5 = -32.6 \]
- For \( y = 73x - 1 \): \[ y = 73(-1.2) - 1 = -87.6 - 1 = -88.6 \]
- These do not match \( 3.3 \).
Since I've calculated all points, and none satisfy both equations, it appears there was a misunderstanding; however, the proper way to find a solution would be to set \( 23x - 5 = 73x - 1 \) and solve for \( x \):
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Set the equations equal: \[ 23x - 5 = 73x - 1 \]
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Rearranging gives: \[ -5 + 1 = 73x - 23x \] \[ -4 = 50x \implies x = -\frac{4}{50} = -\frac{2}{25} \]
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Substitute back to find \( y \): \[ y = 23(-\frac{2}{25}) - 5 = -\frac{46}{25} - \frac{125}{25} = -\frac{171}{25} \]
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You could continue looking for better approximation.
None of the listed points solve both equations. In practical exercises, check for appropriateness of your point listings or calculation methods.