1. The problem is to solve a system of linear equations (SPLDV). 2. A system of linear equations consists of two or more linear equations with the same variables. The goal is to find the values of the variables that satisfy all equations simultaneously. 3. The common methods to solve SPLDV are substitution, elimination, and graphing. Here, we will use the substitution method as an example. 4. Suppose the system is: $$\begin{cases} ax + by = c \\ dx + ey = f \end{cases}$$ 5. Step 1: Solve one equation for one variable. For example, from the first equation: $$x = \frac{c - by}{a}$$ 6. Step 2: Substitute this expression for $x$ into the second equation: $$d\left(\frac{c - by}{a}\right) + ey = f$$ 7. Step 3: Multiply through by $a$ to clear the denominator: $$d(c - by) + aey = af$$ 8. Step 4: Distribute $d$: $$dc - dby + aey = af$$ 9. Step 5: Group terms with $y$: $$(-db + ae)y = af - dc$$ 10. Step 6: Solve for $y$: $$y = \frac{af - dc}{ae - db}$$ 11. Step 7: Substitute $y$ back into the expression for $x$: $$x = \frac{c - b\left(\frac{af - dc}{ae - db}\right)}{a}$$ 12. This gives the solution $(x,y)$ that satisfies both equations. This method can be applied to any SPLDV to find the unique solution if it exists.