Find the solution of the system of equations.
9, x, plus, 6, y, equals, 6
9x+6y=
6
minus, x, minus, 3, y, equals, 11
−x−3y=
11

We are given the following system of linear equations:

1. \( 9x + 6y = 6 \)
2. \( -x - 3y = 11 \)

### Step 1: Solve the second equation for \( x \)

From the second equation \( -x - 3y = 11 \), solve for \( x \):

\[
-x = 11 + 3y
\]
\[
x = -11 - 3y
\]

### Step 2: Substitute this value of \( x \) into the first equation

Substitute \( x = -11 - 3y \) into the first equation \( 9x + 6y = 6 \):

\[
9(-11 - 3y) + 6y = 6
\]
\[
-99 - 27y + 6y = 6
\]
\[
-99 - 21y = 6
\]
\[
-21y = 6 + 99
\]
\[
-21y = 105
\]
\[
y = \frac{105}{-21} = -5
\]

### Step 3: Substitute \( y = -5 \) back into the expression for \( x \)

Substitute \( y = -5 \) into \( x = -11 - 3y \):

\[
x = -11 - 3(-5)
\]
\[
x = -11 + 15 = 4
\]

### Final Solution:
The solution to the system of equations is:
\[
x = 4, \quad y = -5
\]

Would you like further details or explanations?

Here are some related questions you might consider:
1. How can we graphically interpret the solution of a system of equations?
2. What are the different methods for solving systems of linear equations?
3. How does the substitution method compare to the elimination method?
4. How do we verify the solution to a system of equations?
5. What happens when a system of equations has no solution or infinitely many solutions?

**Tip:** Always substitute the solution back into the original equations to verify your answer.

Find the solution of the system of equations: 9x + 6y = 6 and -x - 3y = 11

Learn how to solve the system of linear equations 9x + 6y = 6 and -x - 3y = 11 using the substitution method. This problem covers algebraic concepts, simplification techniques, and is suitable for students in Grades 9-10.

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