Solve the system by substitution.

y, equals, minus, 5, x, minus, 10

*y*=

−5*x*−10

y, equals, minus, 10, x

*y*=

−10*x*

We are given the system of equations:

1. \( y = -5x - 10 \)
2. \( y = -10x \)

To solve by substitution, we substitute one expression for \( y \) into the other equation. Since both equations express \( y \), we can set the two expressions for \( y \) equal to each other:

\[
-5x - 10 = -10x
\]

Now, let's solve for \( x \):

### Step 1: Move all terms involving \( x \) to one side:
\[
-5x + 10x = 10
\]
\[
5x = 10
\]

### Step 2: Solve for \( x \):
\[
x = \frac{10}{5} = 2
\]

### Step 3: Substitute \( x = 2 \) into one of the original equations to solve for \( y \). Let's use the second equation \( y = -10x \):

\[
y = -10(2) = -20
\]

### Solution:
The solution to the system is \( x = 2 \) and \( y = -20 \).

Would you like more details or further clarification?

Here are some related questions to extend this problem:

1. What would the solution be if the second equation were \( y = -10x + 5 \)?
2. Can a system of linear equations have no solutions? How does this occur?
3. How would you graph the system and verify the solution geometrically?
4. What happens if both equations represent the same line?
5. Can you explain how to solve a system of equations by elimination?

**Tip:** Always check your solution by substituting the values of \( x \) and \( y \) into both original equations to ensure they hold true.

Solve the system by substitution.
1. y = -5x - 10
2. y = -10x

Learn how to solve the system of linear equations y = -5x - 10 and y = -10x using the substitution method. This problem focuses on solving linear systems, simplifying expressions, and checking the solution. Suitable for students in Grades 8-10.

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