To determine which point is a solution for the simultaneous inequalities \( y > 4x - 2 \) and \( y \geq -13x + 2 \), you can follow these steps:
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Graph the Inequalities:
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For the inequality \( y > 4x - 2 \):
- The line \( y = 4x - 2 \) is the boundary line. The slope is 4, and the y-intercept is -2.
- This line would be dashed because the inequality is "greater than" (not "greater than or equal to"). The region above this line is the solution area.
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For the inequality \( y \geq -13x + 2 \):
- The line \( y = -13x + 2 \) is also a boundary line. The slope is -13, and the y-intercept is 2.
- This line would be solid because the inequality includes "greater than or equal to". The region at or above this line is the solution area.
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Determine Points:
You would need to check each plotted point against both inequalities to see if they satisfy them.
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Check Each Point:
Check each point (x, y) you observe in the graph against both inequalities.
- Substitute the x and y values into the inequalities to see if they hold true.
- If a point is above the dashed line from the first inequality and at or above the solid line from the second inequality, then it is a solution.
Without the specific points available or the visual, I can't provide an exact solution. However, follow this method with the points on your graph, and you should find the correct point that satisfies both inequalities.
For example, if you find a point at (3, 9):
- Check if \( 9 > 4(3) - 2 \) --> \( 9 > 12 - 2 \) --> \( 9 > 10 \) (false)
- Check if \( 9 \geq -13(3) + 2 \) --> \( 9 \geq -39 + 2 \) --> \( 9 \geq -37 \) (true)
Thus, (3, 9) would not satisfy both.
Continue this for other points until you find a valid pair.
Ultimately, please provide the specific coordinates of the plotted points to receive a definite answer.
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