To find the values of \( y \) for the equation \( 15 = 10x + 5y \) given the values for \( x \) as \(-2, -1, 0, 2, 3\), we'll substitute each value of \( x \) into the equation and solve for \( y \).
Step 1: Solve the equation for \( y \)
Starting from the original equation: \[ 15 = 10x + 5y \]
Rearranging it gives: \[ 5y = 15 - 10x \] \[ y = \frac{15 - 10x}{5} \] \[ y = 3 - 2x \]
Step 2: Calculate \( y \) for each value of \( x \)
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When \( x = -2 \): \[ y = 3 - 2(-2) = 3 + 4 = 7 \]
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When \( x = -1 \): \[ y = 3 - 2(-1) = 3 + 2 = 5 \]
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When \( x = 0 \): \[ y = 3 - 2(0) = 3 - 0 = 3 \]
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When \( x = 2 \): \[ y = 3 - 2(2) = 3 - 4 = -1 \]
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When \( x = 3 \): \[ y = 3 - 2(3) = 3 - 6 = -3 \]
Summary of \( y \) values
- For \( x = -2 \), \( y = 7 \)
- For \( x = -1 \), \( y = 5 \)
- For \( x = 0 \), \( y = 3 \)
- For \( x = 2 \), \( y = -1 \)
- For \( x = 3 \), \( y = -3 \)
Here is a summary of the results:
\[ \begin{align*} x & : -2, -1, 0, 2, 3 \ y & : 7, 5, 3, -1, -3 \ \end{align*} \]