To determine the solution of the equation \(1.5 - 2y = 8\), let's first solve for \(y\).
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Subtract \(1.5\) from both sides: \[ -2y = 8 - 1.5 \] \[ -2y = 6.5 \]
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Now divide by \(-2\): \[ y = \frac{6.5}{-2} \] \[ y = -3.25 \]
Now we know that \(y = -3.25\). To check which student has the correct point \((x, y)\), we only need to examine the \(y\) values given in the options:
- Sam believes \((-4, -7)\)
- Peter believes \((-4, 7)\)
- Mary believes \((4, -7)\)
- Fiona believes \((4, 7)\)
None of the \(y\) values provided in the options match \(y = -3.25\). However, we can see that \(y\) is negative as it is equal to -3.25.
Out of the given possibilities:
- Sam's solution \((-4, -7)\): valid since \(y\) is negative.
- Peter's solution \((-4, 7)\): invalid since \(y\) is positive.
- Mary's solution \((4, -7)\): valid since \(y\) is negative.
- Fiona's solution \((4, 7)\): invalid since \(y\) is positive.
However, the problem asks for a solution to the equation. Since none of the pairs given exactly equal the solution of \((x, -3.25)\), there isn't a correct pair as a solution.
Based on the values of \(y\) alone, the options with negative \(y\) values (Sam and Mary) are the only possibly related to the equation, but they still don't satisfy the equation itself. Thus, while there are candidates with negative \(y\) values, there is no accurate solution from the provided options.