Solve the system by substitution.

y, equals, minus, 5, x, minus, 40

*y*=

−5*x*−40

y, equals, 5, x

*y*=

5*x*

To solve the system of equations by substitution, we have the following two equations:

1. \( y = -5x - 40 \)
2. \( y = 5x \)

### Step 1: Substitute the second equation into the first

Since both equations equal \( y \), we can set them equal to each other:

\[
5x = -5x - 40
\]

### Step 2: Solve for \( x \)

Add \( 5x \) to both sides:

\[
5x + 5x = -40
\]

This simplifies to:

\[
10x = -40
\]

Now, divide both sides by 10:

\[
x = -4
\]

### Step 3: Substitute \( x \) back into one of the equations to find \( y \)

Using the second equation \( y = 5x \):

\[
y = 5(-4) = -20
\]

### Solution

The solution to the system of equations is:

\[
(x, y) = (-4, -20)
\]

### Summary

1. \( x = -4 \)
2. \( y = -20 \)

If you need more details or have any questions, feel free to ask! Here are some related questions you might consider:

1. How would you solve this system using elimination instead of substitution?
2. What are the implications of the solution being a point on a graph?
3. How can you verify that the solution is correct?
4. What would happen if the two equations represented parallel lines?
5. Can you graph the two equations to visualize the solution?

**Tip:** Always check your solutions by substituting the values back into the original equations to ensure they satisfy both equations.

Solve the system by substitution: y = -5x - 40 and y = 5x.

Discover how to solve the system of equations y = -5x - 40 and y = 5x using the substitution method. This comprehensive guide includes step-by-step instructions, key formulas, and the final solution of (x, y) = (-4, -20). Perfect for students in Grades 8-10.

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