Substitute into the first equation: \(2(y + 3) + 3y = 12\).

["Understanding Substitution in Solving Linear Equations: Solving (2(y + 3) + 3y = 12)", "When solving linear equations, one powerful technique is substitution—a method that simplifies complex expressions by replacing variables or parts of equations with simpler forms. In this article, we’ll explore how substitution is effectively applied to solve the equation:", "[\n2(y + 3) + 3y = 12\n]", "---", "### What is Substitution in Algebra?", "Substitution in algebra means replacing a variable or grouped expression with a shorter or simpler equivalent to reduce equation complexity. This is especially useful in equations with parentheses, repeated variables, or nested expressions—like the one above.", "---", "### Step-by-Step Substitution in the Equation", "Step 1: Identify the expression to substitute\nThe equation is:\n[\n2(y + 3) + 3y = 12\n]\nNotice that the expression ((y + 3)) appears in parentheses. Instead of expanding immediately, we substitute (y + 3) with a new variable or simplified form. Here, we’ll treat (y + 3) as a single entity (z), or directly replace it.", "Step 2: Substitute (y + 3 = z)\nLet ( z = y + 3 ). Then the equation becomes:\n[\n2z + 3y = 12\n]", "Now, express (y) in terms of (z):\n[\ny = z - 3\n]", "Step 3: Substitute (y = z - 3) into the equation\nReplace (y) in (2z + 3y = 12):\n[\n2z + 3(z - 3) = 12\n]", "Step 4: Solve the simplified equation\nExpand and simplify:\n[\n2z + 3z - 9 = 12\n\Rightarrow 5z - 9 = 12\n]\nAdd 9 to both sides:\n[\n5z = 21\n]\nDivide by 5:\n[\nz = \frac{21}{5}\n]", "Step 5: Back-substitute to find (y)\nRecall (y = z - 3):\n[\ny = \frac{21}{5} - 3 = \frac{21}{5} - \frac{15}{5} = \frac{6}{5}\n]", "---", "### Final Result", "The solution to the equation\n[\n2(y + 3) + 3y = 12\n]\nis:\n[\ny = \frac{6}{5}\n]", "---", "### Why Use Substitution?", "- Simplifies complexity: By replacing (y + 3) with a variable or expression, the equation becomes easier to handle.\n- Maintains accuracy: Avoiding full expansion prevents arithmetic errors.\n- Builds conceptual understanding: Substitution strengthens algebraic reasoning and prepares students for higher-level problem-solving.", "---", "### Key Takeaway", "Substitution is a fundamental algebraic tool that transforms complicated equations into manageable forms. Whether you're working with linear equations like (2(y + 3) + 3y = 12) or more advanced expressions, strategic substitution streamlines solving steps and enhances clarity.", "---", "### Related Keywords for SEO Optimization\n- substitute into linear equation\n- solving 2(y + 3) + 3y = 12\n- algebra substitution method\n- how to solve equations with parentheses\n- step-by-step equation solving\n- algebra substitution example", "---", "Mastering substitution empowers you to tackle increasingly complex equations with confidence. Start practicing with simple expressions—before long, substitution will become second nature!"]