Add to the first equation: \( 2x + 3y + 12x - 3y = 6 + 15 \).

["Adding the First Equation: Simplify and Solve\nSEO-Optimized Article", "---", "When learning algebra, mastering equation simplification is essential. One common task students encounter is combining like terms and simplifying linear equations—key steps before solving for variables. This article dives into the equation:", "[\n2x + 3y + 12x - 3y = 6 + 15\n]", "Our focus is on adding the terms on the left-hand side (LHS), then simplifying the entire expression to clearly reveal the final form of the equation.", "### Step 1: Recognize Like Terms on the LHS\nThe left-hand side contains two variable components: (2x) and (12x) are like terms because they both involve (x), while (3y) and (-3y) are also like terms involving (y).", "[\n(2x + 12x) + (3y - 3y)\n]", "### Step 2: Combine Like Terms\nNow, add the coefficients of the similar variables:\n- For (x): (2 + 12 = 14)\n- For (y): (3 - 3 = 0)", "So the simplified LHS becomes:", "[\n14x + 0y = 14x\n]", "### Step 3: Simplify the Right-Hand Side (RHS)\nThe right-hand side consists of constants: (6 + 15 = 21)", "### Step 4: Write the Simplified Equation\nPutting it all together, the fully simplified equation is:", "[\n14x = 21\n]", "This step-by-step addition and combination of like terms is critical when preparing to isolate the variable in further steps of equation solving.", "### Why This Simplification Matters\nAdding and combining like terms streamlines equations, reduces complexity, and prepares learners to proceed smoothly to later stages—such as solving for (x) by dividing both sides by 14:", "[\nx = \frac{21}{14} = \frac{3}{2}\n]", "### Conclusion\nSimplifying the equation (2x + 3y + 12x - 3y = 6 + 15) through strategic addition of like terms builds a strong foundation in algebraic manipulation. This foundational skill empowers students to solve equations confidently and accurately, forming a key part of algebra mastery.", "---", "Keywords for SEO:\nalgebra equations, add like terms, simplify linear equations, solve for x, intermediate algebra, combine terms, solve 2x + 3y + 12x - 3y\nMeta Description:\nSimplify the equation (2x + 3y + 12x - 3y = 6 + 15) by combining like terms. Learn step-by-step how to add 2x and 12x, and 3y and -3y, resulting in (14x = 21)—a key step in solving linear equations.", "---", "Get more algebra tips and equation-solving strategies by exploring related articles or mastering key techniques like combining constants and variable terms—your foundation for advanced math!"]