1. **Problem statement:** Solve the system of linear equations using substitution method for part (a): $$\begin{cases} 4x + y = 23 \\ y = 6x + 3 \end{cases}$$ 2. **Formula and method:** Substitution method involves substituting the expression for one variable from one equation into the other equation. 3. **Step 1:** Substitute $y = 6x + 3$ into the first equation: $$4x + (6x + 3) = 23$$ 4. **Step 2:** Simplify the equation: $$4x + 6x + 3 = 23$$ $$10x + 3 = 23$$ 5. **Step 3:** Subtract 3 from both sides: $$10x + \cancel{3} - \cancel{3} = 23 - 3$$ $$10x = 20$$ 6. **Step 4:** Divide both sides by 10: $$\frac{10x}{\cancel{10}} = \frac{20}{\cancel{10}}$$ $$x = 2$$ 7. **Step 5:** Substitute $x=2$ back into $y = 6x + 3$: $$y = 6(2) + 3 = 12 + 3 = 15$$ 8. **Final answer:** $$x = 2, \quad y = 15$$ This completes the solution for part (a).