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Solve each equation for m. Then find the value of m for each value of n.

1. m + 3n = 7;n = -2,0,1
2. -5n = 4m + 8;n = -1,0,1
3.8n = -3m + 1;n = -2,2,4

1 answer

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 \( n \):

  • For \( n = -2 \): \[ m = 7 - 3(-2) = 7 + 6 = 13 \]

  • For \( n = 0 \): \[ m = 7 - 3(0) = 7 - 0 = 7 \]

  • 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 \( n \):

  • For \( n = -1 \): \[ m = \frac{-5(-1) - 8}{4} = \frac{5 - 8}{4} = \frac{-3}{4} = -0.75 \]

  • For \( n = 0 \): \[ m = \frac{-5(0) - 8}{4} = \frac{-8}{4} = -2 \]

  • 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 \( n \):

  • For \( n = -2 \): \[ m = \frac{1 - 8(-2)}{3} = \frac{1 + 16}{3} = \frac{17}{3} \approx 5.67 \]

  • For \( n = 2 \): \[ m = \frac{1 - 8(2)}{3} = \frac{1 - 16}{3} = \frac{-15}{3} = -5 \]

  • For \( n = 4 \): \[ m = \frac{1 - 8(4)}{3} = \frac{1 - 32}{3} = \frac{-31}{3} \approx -10.33 \]

Summary of Results

  1. For equation \( m + 3n = 7 \):

    • \( n = -2 \): \( m = 13 \)
    • \( n = 0 \): \( m = 7 \)
    • \( n = 1 \): \( m = 4 \)

  2. For equation \( -5n = 4m + 8 \):

    • \( n = -1 \): \( m = -0.75 \)
    • \( n = 0 \): \( m = -2 \)
    • \( n = 1 \): \( m = -3.25 \)

  3. For equation \( 8n = -3m + 1 \):

    • \( n = -2 \): \( m \approx 5.67 \)
    • \( n = 2 \): \( m = -5 \)
    • \( n = 4 \): \( m \approx -10.33 \)