Solve the system by substitution.

x, equals, minus, 8, y

*x*=

−8*y*

minus, x, plus, y, equals, 18

−*x*+*y*=

18

We are given the following system of equations:

1. \( x = -8y \)
2. \( -x + y = 18 \)

### Step 1: Substitute \( x = -8y \) into the second equation.
We substitute the expression for \( x \) from equation (1) into equation (2):

\[
-(-8y) + y = 18
\]

### Step 2: Simplify the equation.
\[
8y + y = 18
\]
\[
9y = 18
\]

### Step 3: Solve for \( y \).
\[
y = \frac{18}{9} = 2
\]

### Step 4: Substitute \( y = 2 \) back into the equation \( x = -8y \) to find \( x \).
\[
x = -8(2) = -16
\]

### Final Answer:
The solution to the system is:
\[
x = -16, \quad y = 2
\]

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:
1. Solve the system: \( x = 3y \) and \( -x + y = 5 \).
2. Solve the system: \( x = -2y \) and \( x - y = 7 \).
3. Solve the system: \( 2x = 4y + 3 \) and \( -x + y = -1 \).
4. Solve the system: \( x = 4y + 2 \) and \( 2x - 3y = 10 \).
5. Solve the system: \( x = y + 5 \) and \( 2x - y = 7 \).

**Tip:** In substitution, always aim to isolate one variable in terms of the other to simplify solving the system.

Solve the system by substitution: x = -8y and -x + y = 18.

Learn how to solve the system of equations x = -8y and -x + y = 18 using the substitution method. This step-by-step solution demonstrates the key concepts of solving systems of linear equations, ideal for students in Grades 8-10.

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