Solving by substitution is a method used for solving systems of equations, typically involving two or more equations. The idea is to solve one of the equations for one variable in terms of the others, and then substitute that expression into the second equation to solve for the remaining variable(s).

Here is a step-by-step breakdown of the substitution method:

Steps:

1. Choose one of the equations in the system and solve it for one variable (usually the one that looks easiest to isolate).

   Example: $y = 2x + 3$

2. Substitute the expression for that variable into the other equation(s). This will give you a new equation with only one variable.

   Example: Suppose the second equation is: $3x + 2y = 12$ Substituting $y = 2x + 3$ into the second equation: $3x + 2(2x + 3) = 12$

3. Solve the resulting equation for the remaining variable.

   Simplifying the equation: $3x + 4x + 6 = 12$ $7x + 6 = 12$ Subtract 6 from both sides: $7x = 6$ $x = \frac{6}{7}$

4. Substitute the value of the solved variable back into the original equation to solve for the other variable.

   Substitute $x = \frac{6}{7}$ into $y = 2x + 3$: $y = 2 \left(\frac{6}{7}\right) + 3 = \frac{12}{7} + 3 = \frac{12}{7} + \frac{21}{7} = \frac{33}{7}$

Thus, the solution is: $x = \frac{6}{7}, \quad y = \frac{33}{7}$

Would you like help solving a specific system of equations using substitution? Feel free to share the equations if so!