Part A. To solve the system of linear equations using the substitution method, solve for a variable from one of the equations and then substitute it into the equation. Then solve for the remaining variable.
[tex]\begin{cases}y=3x-5\text{ (1)} \\ y=6x-8\text{ (2)}\end{cases}[/tex]Since in this case, the variable y is already clear in both equations, then you can replace the value of y from the first equation in the second equation and solve for x.
[tex]\begin{gathered} y=6x-8\text{ (2)} \\ 3x-5=6x-8 \\ \text{ Add 5 from both sides of the equation} \\ 3x-5+5=6x-8+5 \\ 3x=6x-3 \\ \text{ Subtract 6x from both sides of the equation} \\ 3x-6x=6x-3-6x \\ -3x=-3 \\ \text{ Divide by -3 into both sides of the equation} \\ \frac{-3x}{-3}=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex]Now replace the value of x in any of the initial equations, for example in the first
[tex]\begin{gathered} y=3x-5\text{ (1)} \\ y=3\cdot1-5 \\ y=3-5 \\ y=-2 \end{gathered}[/tex]Therefore, the solutions of the system of linear equations are
[tex]\begin{cases}x=1 \\ y=-2\end{cases}[/tex]Part B. Graphing the equations, you have
By graphing the equations you can see that the lines representing the equations intersect in the ordered pair that coincides with the solution of the system of linear equations.
