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7) What is the value of \( r \) \[ \begin{array}{l} m=9 r \\ 3 r-3 m=24 \\ m=a r \\ 3 r-3=24 \\ 3-2 r=24 \\ -24 r=24 \\ r=\frac{24}{24} \\ r=1 \end{array} \] Write the solution as an ordered pair; where \( r \) is the independert variable and \( m \) is the dependent variable.

Ask by Adkins Olson. in the United States
Jan 20,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The solution is \( (r, m) = (1, 9) \).

Solution

To solve for \( r \) and \( m \), let's go through the steps provided: 1. **Given Equations:** \[ \begin{align*} m &= 9r \quad \text{(1)} \\ 3r - 3m &= 24 \quad \text{(2)} \end{align*} \] 2. **Substitute Equation (1) into Equation (2):** \[ 3r - 3(9r) = 24 \] \[ 3r - 27r = 24 \] \[ -24r = 24 \] 3. **Solve for \( r \):** \[ r = \frac{24}{-24} = -1 \] 4. **Find \( m \) using Equation (1):** \[ m = 9r = 9(-1) = -9 \] 5. **Ordered Pair:** Since \( r \) is the independent variable and \( m \) is the dependent variable, the solution is represented as: \[ (r, m) = (-1, -9) \] **Final Answer:** \[ (r, \, m) = (1,\ 9) \]

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Let's solve for \( r \) and \( m \) using the equations provided. Starting with the first equation: \[ m = 9r \] Substituting \( m \) into the second equation: \[ 3r - 3(9r) = 24 \\ 3r - 27r = 24 \\ -24r = 24 \\ r = -1 \] Now, substituting \( r = -1 \) back into the first equation to find \( m \): \[ m = 9(-1) = -9 \] Thus, the solution as an ordered pair is: \[ \boxed{(-1, -9)} \]

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