To solve the system of linear equations using the method of substitution, follow these steps:

1. Solve one equation for one variable.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the other variable.
4. Substitute back to find the first variable.

Let's consider the following example system of equations:

2x + 3y = 6 \\ x - y = 4 \end{cases}$$ ### Step 1: Solve one equation for one variable We solve the second equation for $$x$$: $$x - y = 4$$ $$x = y + 4$$ ### Step 2: Substitute this expression into the other equation Substitute $$x = y + 4$$ into the first equation: $$2(y + 4) + 3y = 6$$ ### Step 3: Solve the resulting equation for the other variable Simplify and solve for $$y$$: $$2y + 8 + 3y = 6$$ $$5y + 8 = 6$$ $$5y = -2$$ $$y = -\frac{2}{5}$$ ### Step 4: Substitute back to find the first variable Substitute $$y = -\frac{2}{5}$$ back into $$x = y + 4$$: $$x = -\frac{2}{5} + 4$$ $$x = -\frac{2}{5} + \frac{20}{5}$$ $$x = \frac{18}{5}$$ Thus, the solution to the system is: $$\left( \frac{18}{5}, -\frac{2}{5} \right)$$ So the solution in the format requested is: $$\left( \frac{18}{5}, -\frac{2}{5} \right)$$ Would you like more details or have any questions about this solution? Here are 5 questions you might want to ask: 1. Can you explain the substitution method in more detail? 2. How do you check if a system has no solutions? 3. What are some other methods for solving systems of linear equations? 4. How can I verify the solution to a system of linear equations? 5. What does it mean when a system has infinitely many solutions? **Tip:** When substituting expressions, carefully simplify and solve each step to avoid errors.