\begin{aligned}
&-5x+4y = 3\\\\
&x=2y-15
\end{aligned}

We have the system of equations:

\[
\begin{aligned}
-5x + 4y &= 3 \\
x &= 2y - 15
\end{aligned}
\]

### Step 1: Substitute \( x = 2y - 15 \) into the first equation.

\[
-5(2y - 15) + 4y = 3
\]

Expanding:

\[
-10y + 75 + 4y = 3
\]

\[
-6y + 75 = 3
\]

### Step 2: Solve for \( y \)

\[
-6y = 3 - 75
\]

\[
-6y = -72
\]

\[
y = 12
\]

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

Substituting \( y = 12 \) into \( x = 2y - 15 \):

\[
x = 2(12) - 15
\]

\[
x = 24 - 15
\]

\[
x = 9
\]

### Final Answer:

\[
(x, y) = (9, 12)
\]

Would you like a step-by-step breakdown of any part?  

Here are some related questions to explore:  
1. How do you check if your solution to a system of equations is correct?  
2. What methods can be used to solve systems of equations besides substitution?  
3. How do you solve a system of equations graphically?  
4. What happens if a system of equations has no solution or infinite solutions?  
5. How can you solve a system of equations using matrices?  

**Tip:** Always substitute your solution back into the original equations to verify correctness!

Learn how to solve the system of equations -5x + 4y = 3 and x = 2y - 15 step-by-step using the substitution method. This problem covers key algebraic concepts such as solving linear equations and substitution. Suitable for students in Grades 8-10.

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