1. **State the problem:** Solve the system of linear equations: $$20 = 2x - y$$ $$x + y = 34$$ Find the values of $x$ and $y$ that satisfy both equations simultaneously. 2. **Write the system clearly:** $$2x - y = 20$$ $$x + y = 34$$ 3. **Add the two equations to eliminate $y$:** $$ (2x - y) + (x + y) = 20 + 34 $$ $$ 2x - y + x + y = 54 $$ $$ 3x = 54 $$ 4. **Solve for $x$:** $$ x = \frac{54}{3} $$ $$ x = 18 $$ 5. **Substitute $x=18$ into the second equation to find $y$:** $$ 18 + y = 34 $$ $$ y = 34 - 18 $$ $$ y = 16 $$ 6. **Final answer:** The solution to the system is $x=18$, $y=16$. This means the two lines intersect at the point $(18,16)$.