x+y＝1000000，x/0.13*1.13+y/0.03*1.03＝82568.81

We are given the following system of equations:

1. \( x + y = 1,000,000 \)
2. \( \frac{x}{0.13} \times 1.13 + \frac{y}{0.03} \times 1.03 = 82,568.81 \)

### Step 1: Simplify the second equation

Let's simplify the second equation step by step.

\[
\frac{x}{0.13} \times 1.13 = \frac{1.13x}{0.13}
\]
\[
\frac{y}{0.03} \times 1.03 = \frac{1.03y}{0.03}
\]

So the second equation becomes:

\[
\frac{1.13x}{0.13} + \frac{1.03y}{0.03} = 82,568.81
\]

Now simplify the constants:

\[
\frac{1.13}{0.13} = 8.6923 \quad \text{and} \quad \frac{1.03}{0.03} = 34.3333
\]

Thus, the equation becomes:

\[
8.6923x + 34.3333y = 82,568.81
\]

### Step 2: Solve the system of equations

We now have the system:

1. \( x + y = 1,000,000 \)
2. \( 8.6923x + 34.3333y = 82,568.81 \)

We can solve this using substitution or elimination. Let's use substitution.

From the first equation, solve for \( y \):

\[
y = 1,000,000 - x
\]

Substitute this expression for \( y \) into the second equation:

\[
8.6923x + 34.3333(1,000,000 - x) = 82,568.81
\]

Now simplify:

\[
8.6923x + 34,333,300 - 34.3333x = 82,568.81
\]

Combine like terms:

\[
-25.641x + 34,333,300 = 82,568.81
\]

Now solve for \( x \):

\[
-25.641x = 82,568.81 - 34,333,300
\]
\[
-25.641x = -34,250,731.19
\]
\[
x = \frac{-34,250,731.19}{-25.641} = 1,335,836.50
\]

### Step 3: Solve for \( y \)

Now that we know \( x = 1,335,836.50 \), substitute this back into \( y = 1,000,000 - x \):

\[
y = 1,000,000 - 1,335,836.50 = -335,836.50
\]

### Final Answer:
\[
x = 1,335,836.50, \quad y = -335,836.50
\]

Let me know if you'd like further details or clarification!

---

Here are 5 related questions to expand on this:

1. What happens if the coefficients of the second equation change slightly?
2. How would you solve this system using matrix methods?
3. Can this problem be solved graphically, and how would it look on a graph?
4. How would the solution change if \( x + y \) were a different number?
5. What is the significance of negative \( y \) in this context?

**Tip:** When solving systems of equations, substitution is often useful when one variable is easy to isolate, while elimination works well when combining equations to cancel out variables.

x + y = 1000000, x/0.13*1.13 + y/0.03*1.03 = 82568.81

This solution tackles the system of equations: x + y = 1,000,000 and x/0.13*1.13 + y/0.03*1.03 = 82,568.81. Detailed steps include simplifying the second equation and using substitution to solve for x and y. This problem is ideal for high school students in Grades 10-12.

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