M + D = 30
M + 8 = 4x (D + 8)
what is the value of M and D

We are given the following system of equations:

1. \( M + D = 30 \)
2. \( M + 8 = 4(D + 8) \)

### Step 1: Solve the first equation for \( M \)
From the first equation:

\[
M = 30 - D
\]

### Step 2: Substitute \( M = 30 - D \) into the second equation
Now, substitute \( M = 30 - D \) into the second equation:

\[
(30 - D) + 8 = 4(D + 8)
\]

This simplifies to:

\[
38 - D = 4(D + 8)
\]

### Step 3: Expand and solve for \( D \)
Expand the right-hand side:

\[
38 - D = 4D + 32
\]

Now, move all the terms involving \( D \) to one side:

\[
38 - 32 = 4D + D
\]

Simplifying:

\[
6 = 5D
\]

Thus:

\[
D = \frac{6}{5} = 1.2
\]

### Step 4: Substitute \( D = 1.2 \) back into the first equation
Now substitute \( D = 1.2 \) into the first equation:

\[
M + 1.2 = 30
\]

Solving for \( M \):

\[
M = 30 - 1.2 = 28.8
\]

### Final Answer:
- \( M = 28.8 \)
- \( D = 1.2 \)

Would you like any additional details or have any questions?

Here are 5 related questions:
1. What happens if we change the constant in the second equation?
2. How would the solution change if the first equation were \( M + D = 40 \)?
3. Can we graph these two equations to visually check the solution?
4. What is the effect of multiplying both sides of the second equation by 2 instead of 4?
5. How can we check if the values of \( M \) and \( D \) are correct?

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

M + D = 30
M + 8 = 4x (D + 8)
what is the value of M and D?

Learn how to solve a system of linear equations: M + D = 30 and M + 8 = 4(D + 8). This step-by-step guide uses substitution to find the values of M and D, ideal for students in Grades 8-10.

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