1. **Problem 1:** Solve the system by elimination: $$\begin{cases} 2x + y = 6 \\ 2x - y = 2 \end{cases}$$ 2. Add the two equations to eliminate $y$: $$ (2x + y) + (2x - y) = 6 + 2 $$ $$ 4x + \cancel{y} - \cancel{y} = 8 $$ $$ 4x = 8 $$ 3. Solve for $x$: $$ x = \frac{8}{4} = 2 $$ 4. Substitute $x=2$ into the first equation: $$ 2(2) + y = 6 $$ $$ 4 + y = 6 $$ $$ y = 6 - 4 = 2 $$ 5. **Solution for Problem 1:** $$ (x, y) = (2, 2) $$ --- Since the user asked for step-by-step solution and there are 5 distinct problems, but per GUEST RULE only solve the first completely, set q_count=5.