Solve the ecuation system: Ecuación 1:  m + r = 29.04
Ecuación 2:    r − m = 4.62

To solve the system of equations, we can use the method of addition or substitution. Here, we'll use the method of addition to eliminate one of the variables.

Given equations:
1. \( m + r = 29.04 \)
2. \( r - m = 4.62 \)

Let's add these two equations:

\[ (m + r) + (r - m) = 29.04 + 4.62 \]

This simplifies to:

\[ m + r + r - m = 29.04 + 4.62 \]

\[ 2r = 33.66 \]

Now, solve for \( r \):

\[ r = \frac{33.66}{2} \]

\[ r = 16.83 \]

Next, substitute \( r = 16.83 \) back into the first equation to solve for \( m \):

\[ m + 16.83 = 29.04 \]

\[ m = 29.04 - 16.83 \]

\[ m = 12.21 \]

So, the solutions are:

\[ m = 12.21 \]
\[ r = 16.83 \]

Would you like any more details or have any questions?

Here are some more questions you might be interested in:

1. How do you solve a system of equations using substitution?
2. What are other methods to solve systems of linear equations?
3. Can you explain the concept of matrices in solving linear systems?
4. How do you graphically solve a system of linear equations?
5. What are the applications of systems of equations in real life?

**Tip:** When solving systems of equations, always double-check your solutions by substituting them back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of equations: m + r = 29.04, r - m = 4.62 with a detailed step-by-step solution. This problem covers methods of solving linear equations and substitution. Suitable for students in Grades 9-12.

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