Let's solve each equation for \( m \) and then find the corresponding values for each specified value of \( n \).
1. Solve \( m + 3n = 7 \)
To solve for \( m \), we rearrange the equation:
\[ m = 7 - 3n \]
Now we will find \( m \) for each specified value of \( n \):
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For \( n = -2 \): \[ m = 7 - 3(-2) = 7 + 6 = 13 \]
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For \( n = 0 \): \[ m = 7 - 3(0) = 7 - 0 = 7 \]
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For \( n = 1 \): \[ m = 7 - 3(1) = 7 - 3 = 4 \]
2. Solve \( -5n = 4m + 8 \)
First, rearrange the equation to express \( m \) in terms of \( n \):
\[ 4m = -5n - 8 \] \[ m = \frac{-5n - 8}{4} \]
Now we will find \( m \) for each specified value of \( n \):
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For \( n = -1 \): \[ m = \frac{-5(-1) - 8}{4} = \frac{5 - 8}{4} = \frac{-3}{4} = -0.75 \]
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For \( n = 0 \): \[ m = \frac{-5(0) - 8}{4} = \frac{-8}{4} = -2 \]
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For \( n = 1 \): \[ m = \frac{-5(1) - 8}{4} = \frac{-5 - 8}{4} = \frac{-13}{4} = -3.25 \]
3. Solve \( 8n = -3m + 1 \)
First, rearrange the equation to solve for \( m \):
\[ -3m = 8n - 1 \] \[ m = \frac{1 - 8n}{3} \]
Now we will find \( m \) for each specified value of \( n \):
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For \( n = -2 \): \[ m = \frac{1 - 8(-2)}{3} = \frac{1 + 16}{3} = \frac{17}{3} \approx 5.67 \]
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For \( n = 2 \): \[ m = \frac{1 - 8(2)}{3} = \frac{1 - 16}{3} = \frac{-15}{3} = -5 \]
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For \( n = 4 \): \[ m = \frac{1 - 8(4)}{3} = \frac{1 - 32}{3} = \frac{-31}{3} \approx -10.33 \]
Summary of Results
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For equation \( m + 3n = 7 \):
- \( n = -2 \): \( m = 13 \)
- \( n = 0 \): \( m = 7 \)
- \( n = 1 \): \( m = 4 \)
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For equation \( -5n = 4m + 8 \):
- \( n = -1 \): \( m = -0.75 \)
- \( n = 0 \): \( m = -2 \)
- \( n = 1 \): \( m = -3.25 \)
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For equation \( 8n = -3m + 1 \):
- \( n = -2 \): \( m \approx 5.67 \)
- \( n = 2 \): \( m = -5 \)
- \( n = 4 \): \( m \approx -10.33 \)