1. **State the problem:** Solve the system of linear equations: $$3x - y = 4$$ $$7x + 2y = 18$$ 2. **Choose a method:** We will use the substitution or elimination method. Here, elimination is convenient. 3. **Make coefficients of $y$ equal:** Multiply the first equation by 2 to align the $y$ terms: $$2(3x - y) = 2(4) \Rightarrow 6x - 2y = 8$$ 4. **Write the new system:** $$6x - 2y = 8$$ $$7x + 2y = 18$$ 5. **Add the two equations to eliminate $y$:** $$ (6x - 2y) + (7x + 2y) = 8 + 18 $$ $$ 6x + 7x + (-2y + 2y) = 26 $$ $$ 13x + 0 = 26 $$ $$ 13x = 26 $$ 6. **Solve for $x$:** $$ x = \frac{26}{13} $$ $$ x = 2 $$ 7. **Substitute $x=2$ into the first original equation to find $y$:** $$ 3(2) - y = 4 $$ $$ 6 - y = 4 $$ 8. **Solve for $y$:** $$ -y = 4 - 6 $$ $$ -y = -2 $$ $$ y = 2 $$ 9. **Final solution:** $$ (x, y) = (2, 2) $$ This means the two lines intersect at the point $(2, 2)$, which is the solution to the system.