https://file.aiquickdraw.com/mathbot/file/17268662804010petnwyo.jpg

The system of linear equations provided in the image is:

1. \( 8x + 3y = 13 \)
2. \( 3x + 2y = 11 \)

To solve this system, we can use the method of elimination or substitution. I'll demonstrate using the elimination method:

First, we'll eliminate \(y\) by making the coefficients of \(y\) in both equations equal. To do this, multiply the first equation by 2 and the second equation by 3:

\[ 16x + 6y = 26 \] (Equation 1 multiplied by 2)
\[ 9x + 6y = 33 \] (Equation 2 multiplied by 3)

Now subtract the first modified equation from the second:

\[ (9x + 6y) - (16x + 6y) = 33 - 26 \]
\[ -7x = 7 \]
\[ x = -1 \]

Now substitute \( x = -1 \) back into the second original equation to solve for \( y \):

\[ 3(-1) + 2y = 11 \]
\[ -3 + 2y = 11 \]
\[ 2y = 14 \]
\[ y = 7 \]

Thus, the solution to the system of equations is \( x = -1 \) and \( y = 7 \).

Would you like a more detailed explanation on any step? Do you have any other questions about this solution?

Here are some additional related questions you might find interesting:
1. How would the solution change if one of the coefficients were different?
2. What if the system had no solutions or infinitely many solutions?
3. How would you solve this system using the substitution method?
4. Can you graph these equations to visually find the solution?
5. What are the implications of changing one of the equations to an inequality?

**Tip**: When solving systems of equations, always check your solutions by substituting the values back into the original equations to ensure they satisfy both equations.

Solve the system of equations: 8x + 3y = 13 and 3x + 2y = 11.

Learn how to solve the system of linear equations 8x + 3y = 13 and 3x + 2y = 11 using the elimination method. This problem covers key algebraic concepts and is suitable for students in Grades 8-10.

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