1. **State the problem:** We are given the system of equations: $$4x + 3y = 6$$ $$y = 2x - 4$$ We want to find the solution to this system, i.e., the values of $x$ and $y$ that satisfy both equations simultaneously. 2. **Use substitution method:** Since the second equation is already solved for $y$, substitute $y = 2x - 4$ into the first equation: $$4x + 3(2x - 4) = 6$$ 3. **Simplify and solve for $x$:** $$4x + 6x - 12 = 6$$ $$10x - 12 = 6$$ Add 12 to both sides: $$10x - \cancel{12} + \cancel{12} = 6 + 12$$ $$10x = 18$$ Divide both sides by 10: $$\frac{10x}{\cancel{10}} = \frac{18}{\cancel{10}}$$ $$x = \frac{18}{10} = \frac{9}{5}$$ 4. **Find $y$ using the value of $x$:** Substitute $x = \frac{9}{5}$ into $y = 2x - 4$: $$y = 2 \times \frac{9}{5} - 4 = \frac{18}{5} - 4 = \frac{18}{5} - \frac{20}{5} = -\frac{2}{5}$$ 5. **Final answer:** The solution to the system is: $$\boxed{\left(\frac{9}{5}, -\frac{2}{5}\right)}$$ This means the two lines intersect at the point $\left(\frac{9}{5}, -\frac{2}{5}\right)$. --- **Summary:** - Substitute $y$ from the second equation into the first. - Solve for $x$. - Substitute $x$ back to find $y$. - The solution is the point where both lines intersect.