Let's solve the given system of equations using substitution. The system is:

-2x + y = -3 \tag{1} 5x - 3y = 5 \tag{2}

Step 1: Solve one equation for one variable

From equation (1), we can solve for $y$ in terms of $x$:

y = 2x - 3 \tag{3}

Step 2: Substitute $y$ into the second equation

Now, substitute equation (3) into equation (2):

$5x - 3(2x - 3) = 5$

Step 3: Simplify and solve for $x$

Expand the equation:

$5x - 6x + 9 = 5$

Combine like terms:

$-x + 9 = 5$

Subtract 9 from both sides:

$-x = -4$

Solve for $x$:

$x = 4$

Step 4: Substitute $x = 4$ into the expression for $y$

Substitute $x = 4$ into equation (3):

$y = 2(4) - 3 = 8 - 3 = 5$

Final Solution:

The solution to the system is: $x = 4, \quad y = 5$

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:

1. Can you solve the same system using the elimination method?
2. How does substitution differ from elimination in terms of strategy?
3. What happens if the system of equations has no solution or infinitely many solutions?
4. Can substitution be used for non-linear systems? If so, how?
5. How can you check if your solution is correct for any system of equations?

Tip: After solving a system, always substitute the values back into the original equations to verify your solution.