To solve the system using substitution, let's proceed with the equations given:

1. Equations:
   • $y = 2x + 1$
   • $5x + 3y = 25$

Step-by-Step Solution:

1. Substitute $y = 2x + 1$ into the second equation: $5x + 3(2x + 1) = 25$

2. Expand and simplify: $5x + 6x + 3 = 25$ $11x + 3 = 25$

3. Solve for $x$: $11x = 25 - 3$ $11x = 22$ $x = 2$

4. Substitute $x = 2$ back into $y = 2x + 1$: $y = 2(2) + 1$ $y = 4 + 1$ $y = 5$

Solution:

The solution to the system is:

• $x = 2$
• $y = 5$

Would you like a more detailed explanation on substitution? Here are a few related questions to explore:

1. How does substitution work in solving systems of equations?
2. What other methods can solve a system of linear equations?
3. How do we interpret the solution of a system in a graphical context?
4. Can substitution be used for nonlinear systems of equations?
5. What if both equations were in terms of $y$; could substitution still work?

Tip: Always check your solution by substituting both values back into the original equations to verify they satisfy both.