To solve a system of equations by substitution, follow these steps:

Example System of Equations:

1. $y = 2x + 3$
2. $3x + y = 12$

Steps:

1. Solve one equation for one variable (if not already done):
   Equation 1 already expresses $y$ in terms of $x$:
   $y = 2x + 3$.

2. Substitute this expression into the other equation:
   Replace $y$ in Equation 2 with $2x + 3$:
   $3x + (2x + 3) = 12$.

3. Solve for the remaining variable:
   Combine like terms:
   $3x + 2x + 3 = 12$
   $5x + 3 = 12$.
   Subtract 3 from both sides:
   $5x = 9$.
   Divide by 5:
   $x = \frac{9}{5}$.

4. Substitute back to find the other variable:
   Substitute $x = \frac{9}{5}$ into $y = 2x + 3$:
   $y = 2\left(\frac{9}{5}\right) + 3$.
   $y = \frac{18}{5} + \frac{15}{5} = \frac{33}{5}$.

Final Solution:

The solution is: $x = \frac{9}{5}, \quad y = \frac{33}{5}$

Would you like to go through more examples or any particular scenario?

5 Related Questions:

1. What is the graphical interpretation of solving systems of equations by substitution?
2. How does substitution compare to the elimination method?
3. Can substitution be used for non-linear systems of equations?
4. How do you handle systems with no solution or infinitely many solutions using substitution?
5. What are common mistakes to avoid in the substitution method?

Tip:

Always simplify one equation to isolate one variable before substitution to make the process efficient and less error-prone.