First, solve the second equation for \( y \):

["Title: How to Solve the Second Equation for ( y ): A Step-by-Step Guide", "Meta Description:\nLearn how to solve the second linear equation for ( y ) with clear examples and proven methods. Perfect for students mastering algebra!", "---", "### Introduction", "Mastering algebra requires not only understanding mathematical concepts but also applying step-by-step problem-solving techniques. One essential skill is solving equations for a particular variable—especially isolating ( y ). Whether you’re tackling basic linear equations or more complex systems, knowing how to solve the second equation for ( y ) empowers you to confidently handle various math challenges.", "In this article, we’ll explore how to solve the second equation for ( y ) using clear, logical steps—ideal for students, educators, and anyone looking to strengthen their algebraic fundementals.", "---", "### Why Solving for ( y ) Matters", "In algebra, equations often list multiple variables. Solving one equation for ( y ) sets the groundwork for substituting that expression into another equation, solving systems, and graphing linear relationships. Mastering this skill enhances your ability to:", "- Simplify systems of equations\n- Interpret real-world problems modeled with equations\n- Build confidence in higher-level math", "---", "### Step-by-Step Guide: Solving the Second Equation for ( y )", "Let’s walk through the general process using a sample second equation. Suppose your second equation is:", "[\n3x + 2y = 12\n]", "Goal: Isolate ( y ) on one side of the equation.", "#### Step 1: Move all terms not containing ( y ) to the other side", "Starting with:", "[\n3x + 2y = 12\n]", "Subtract ( 3x ) from both sides:", "[\n2y = 12 - 3x\n]", "Rationale: We eliminated ( x ) from the left side to prepare to isolate ( y ).", "#### Step 2: Divide both sides by the coefficient of ( y )", "Now divide each side by 2:", "[\ny = \frac{12 - 3x}{2}\n]", "This gives ( y ) expressed purely in terms of ( x ).", "#### Step 3 (Optional): Simplify the expression", "You can split the fraction:", "[\ny = 6 - \frac{3}{2}x\n]", "This form emphasizes the slope and intercept if graphing.", "---", "### Practical Example", "Suppose ( x = 2 ). Substitute into the isolated equation:", "[\ny = 6 - \frac{3}{2}(2) = 6 - 3 = 3\n]", "Just like in the second equation, we systematically eliminated other terms and divided—proving the power of step-by-step substitution.", "---", "### Tips for Success", "- Always isolate the term with ( y ) first.\n- Use operations (addition, subtraction, multiplication, division) equally on both sides to maintain balance.\n- Simplify fractions when possible to avoid complex expressions.\n- Verify your solution by plugging ( y ) back into the original equation.", "---", "### Real-World Application", "Imagine a budgeting problem modeled by:", "[\n2x + 5y = 50\n]", "Solving for ( y ):", "[\ny = \frac{50 - 2x}{5}\n]", "This allows you to decide how to allocate funds between ( x ) and ( y )—demonstrating algebra’s practical use.", "---", "### Conclusion", "Solving the second equation for ( y ) is a foundational skill that opens doors to systems of equations, graphing, and real-world problem solving. By following a clear process—eliminate other terms, divide evenly, and simplify—you unlock algebraic fluency essential for academic and everyday success.", "---", "Key Takeaways:\n- Isolate ( y ) in a linear equation.\n- Use inverse operations to maintain equality.\n- Simplify the expression for clarity.\n- Always verify your solution.", "---", "Call to Action:\nPractice isolating ( y ) in different equations—start with simple forms and progress to more complex ones. Master this skill today, and watch your algebra confidence soar!", "#### Related Search Terms:\n- How to solve second equation for y algebra\n- Isolate y step-by-step\n- Linear equation y isolation guide\n- Solve for y explained clearly", "---", "Investing time in mastering algebraic isolation pays lifelong dividends. Start solving equations today!"]