Since $y = 3x$ is already solved for $y$, substitute into the second equation:

Step 1: Substitute $x + (3x) = 12$

Step 2: Solve for $x$ $4x = 12$ $x = 3$

Step 3: Find $y$ using $y = 3x$ $y = 3(3) = 9$

Check: $3 + 9 = 12$ ✓

Answer: $(3, 9)$

Notice the $y$ coefficients are opposites, so we can add the equations:

Step 1: Add the equations $\begin{array}{r} 3x + 2y = 16 \\ + \quad 2x - 2y = 4 \\ \hline 5x = 20 \end{array}$

Step 2: Solve for $x$ $x = 4$

Step 3: Substitute $x = 4$ into the first equation $3(4) + 2y = 16$ $12 + 2y = 16$ $2y = 4$ $y = 2$

Answer: $(4, 2)$

Step 1: Notice that if we multiply the first equation by 2: $2(2x + 3y) = 2(7)$ $4x + 6y = 14$

Step 2: Compare with the second equation: $4x + 6y = 14$ $4x + 6y = 10$

This says the same expression equals two different numbers, which is impossible!

Answer: No solution (the lines are parallel and never intersect)