Solve the system by substitution.

x, minus, 5, y, equals, minus, 11

*x*−5*y*=

−11

minus, 6, y, equals, x

−6*y*=

*x*

Let's solve this system of equations using substitution. The system is:

1. \( x - 5y = -11 \)
2. \( -6y = x \)

### Step 1: Solve one equation for one variable
Let's solve the second equation for \( x \):

\[
x = -6y
\]

### Step 2: Substitute into the first equation
Now, substitute \( x = -6y \) into the first equation:

\[
-6y - 5y = -11
\]

Simplify:

\[
-11y = -11
\]

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

\[
y = \frac{-11}{-11} = 1
\]

So, \( y = 1 \).

### Step 4: Substitute \( y = 1 \) into \( x = -6y \)

Substitute \( y = 1 \) into the expression \( x = -6y \):

\[
x = -6(1) = -6
\]

### Final Solution:

The solution to the system is:

\[
x = -6, \quad y = 1
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions to expand your understanding:
1. How do you solve a system of equations using elimination instead of substitution?
2. What happens if both equations are dependent or inconsistent?
3. Can you explain how to graphically solve a system of equations?
4. What are the possible types of solutions for a system of linear equations?
5. How can substitution be applied to nonlinear systems of equations?

**Tip**: Always check your solution by substituting both values into the original equations to verify your work!

Solve the system by substitution.
x - 5y = -11
-6y = x

Learn how to solve the system of equations x - 5y = -11 and -6y = x using the substitution method. This detailed step-by-step solution covers key algebraic concepts like substitution and solving linear equations, perfect for students in Grades 8-10.

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