Step 1: The coefficients of y are +3 and −3, which are equal and opposite, so adding the equations removes y. Step 2: Add: (2x + 4x) + (3y − 3y) = 12 + 6, so 6x = 18 and x = 3. Step 3: Substitute x = 3 in 2x + 3y = 12: 6 + 3y = 12, so 3y = 6 and y = 2. Step 4: Verify in the second equation: 4(3) − 3(2) = 12 − 6 = 6 ✓. Answer: y is eliminated; x = 3, y = 2.