To determine a solution for the equation \( 1.5x - 2y = 8 \), you can solve for one variable in terms of the other. Here, we'll solve for \( y \) in terms of \( x \):
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Start with the original equation:
\[ 1.5x - 2y = 8 \]
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Rearrange the equation to isolate \( y \):
\[ -2y = 8 - 1.5x \]
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Divide everything by -2 to solve for \( y \):
\[ y = \frac{1.5x - 8}{2} \]
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Simplify:
\[ y = 0.75x - 4 \]
Now you have \( y \) expressed in terms of \( x \). You can choose any value for \( x \) to find a corresponding value for \( y \). Here are a few example solutions:
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If \( x = 0 \):
\[ y = 0.75(0) - 4 = -4 \quad \Rightarrow \quad (0, -4) \]
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If \( x = 4 \):
\[ y = 0.75(4) - 4 = 3 - 4 = -1 \quad \Rightarrow \quad (4, -1) \]
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If \( x = 8 \):
\[ y = 0.75(8) - 4 = 6 - 4 = 2 \quad \Rightarrow \quad (8, 2) \]
These points (0, -4), (4, -1), and (8, 2) are all solutions to the equation \( 1.5x - 2y = 8 \).