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We are given a system of equations:

\[
-3x + y = 9
\]
\[
2x + 3y = 5
\]

The first equation is to be solved for \( y \). Let's rearrange it:

\[
y = 9 + 3x
\]

Now, we will substitute this value of \( y \) into the second equation to find \( x \):

\[
2x + 3(9 + 3x) = 5
\]

Expanding the equation:

\[
2x + 27 + 9x = 5
\]

Combining like terms:

\[
11x + 27 = 5
\]

Subtracting 27 from both sides:

\[
11x = 5 - 27
\]
\[
11x = -22
\]

Dividing by 11:

\[
x = -2
\]

Now substitute \( x = -2 \) back into the equation for \( y \):

\[
y = 9 + 3(-2) = 9 - 6 = 3
\]

So the solution to the system is \( (x, y) = (-2, 3) \).

Let me know if you would like more details! Here are some related questions to extend this topic:

1. How do you solve a system of equations using substitution?
2. Can you solve this system using the elimination method?
3. What happens if the system has no solution or infinitely many solutions?
4. How do you graphically represent a system of equations?
5. What is the difference between consistent and inconsistent systems?

**Tip:** Always verify your solution by plugging the values of \( x \) and \( y \) back into the original equations.

-3x + y = 9, 2x + 3y = 5. First equation solved for y.

Learn how to solve the system of equations -3x + y = 9 and 2x + 3y = 5 using the substitution method. Follow a step-by-step approach to find the solution (x, y) = (-2, 3), suitable for students in Grades 8-10.

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