1. **Problem Statement:** Solve the system of simultaneous equations using the substitution method. 2. **General Idea:** The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. 3. **Step-by-step:** - Suppose we have two equations: $$\begin{cases} x + y = 5 \\ 2x - y = 1 \end{cases}$$ - Step 1: Solve the first equation for $y$: $$y = 5 - x$$ - Step 2: Substitute $y = 5 - x$ into the second equation: $$2x - (5 - x) = 1$$ - Step 3: Simplify the substituted equation: $$2x - 5 + x = 1$$ $$3x - 5 = 1$$ - Step 4: Solve for $x$: $$3x = 1 + 5$$ $$3x = 6$$ $$x = \frac{6}{3}$$ $$x = 2$$ - Step 5: Substitute $x = 2$ back into $y = 5 - x$: $$y = 5 - 2$$ $$y = 3$$ 4. **Final answer:** $$x = 2, \quad y = 3$$ This means the solution to the system is the point $(2,3)$ where both equations intersect. 5. **Summary:** - Solve one equation for one variable. - Substitute into the other equation. - Solve for the remaining variable. - Substitute back to find the other variable. This method works well when one equation is easy to solve for one variable.