https://file.aiquickdraw.com/mathbot/file/1726656098877iub7jlla.jpg

The system of equations in the image you provided is as follows:

1. \( y = 6x + 11 \)
2. \( 2x - 3y = 7 \)

We can solve this system using substitution since the first equation is already solved for \(y\).

### Steps to solve:

1. **Substitute \( y = 6x + 11 \) into the second equation**:
   \[
   2x - 3(6x + 11) = 7
   \]
   Simplify this:
   \[
   2x - 18x - 33 = 7
   \]
   Combine like terms:
   \[
   -16x - 33 = 7
   \]
   Add 33 to both sides:
   \[
   -16x = 40
   \]
   Divide by -16:
   \[
   x = -\frac{40}{16} = -\frac{5}{2}
   \]

2. **Substitute \( x = -\frac{5}{2} \) into \( y = 6x + 11 \)**:
   \[
   y = 6\left(-\frac{5}{2}\right) + 11
   \]
   Simplify:
   \[
   y = -15 + 11 = -4
   \]

### Solution:
The solution to the system of equations is:
\[
x = -\frac{5}{2}, \quad y = -4
\]

Would you like more details or explanations on the steps? Here are five related questions to extend your understanding:

1. How can you

Solve the system of equations: y = 6x + 11 and 2x - 3y = 7

Learn how to solve the system of equations y = 6x + 11 and 2x - 3y = 7 using substitution. Follow a detailed step-by-step approach for solving algebraic linear equations. This lesson covers key concepts such as slope-intercept form and the substitution method. Ideal for students in Grades 8-10.

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