Substitute $ y = 10 - x $ into the second equation:

["# How to Substitute ( y = 10 - x ) into the Second Equation: A Step-by-Step SEO Guide", "When solving systems of equations, substitution is one of the most powerful and widely used techniques. In this article, we’ll explore how to effectively substitute ( y = 10 - x ) into the second equation in a system, with a focus on clarity, correctness, and search engine optimization (SEO). Whether you're a student, educator, or self-learner, understanding how to properly perform substitution enhances your algebra skills and prepares you for more advanced math challenges.", "## What It Means to Substitute in Equations", "Substitution involves replacing a variable or expression in one equation with its equivalent from another equation. This method simplifies the system by reducing the number of variables, making it easier to solve for one variable at a time.", "In many problems, especially geometry and linear equations, substituting one variable using a linear expression helps convert a system into a single-variable equation—ideal for solving.", "## The Role of ( y = 10 - x ) in Equation Substitution", "Consider a system where one equation defines ( y ) in terms of ( x ), such as:", "[\ny = 10 - x\n]", "This equation relates ( y ) linearly to ( x ), making it perfect for substitution into another equation. For example, suppose your second equation is:", "[\n5x + 2y = 40\n]", "Instead of trying to solve both equations simultaneously with two variables, substitute ( y = 10 - x ) into this second equation:", "### Step-by-Step Substitution", "1. Start with the original second equation:", "[\n5x + 2y = 40\n]", "2. Substitute ( y ) with ( 10 - x ):", "[\n5x + 2(10 - x) = 40\n]", "3. Simplify the expression:", "[\n5x + 20 - 2x = 40\n]", "4. Combine like terms:", "[\n(5x - 2x) + 20 = 40 \implies 3x + 20 = 40\n]", "5. Isolate ( x ):", "[\n3x = 40 - 20 \implies 3x = 20\n]", "[\nx = \frac{20}{3}\n]", "6. Find ( y ):", "Substitute ( x = \frac{20}{3} ) back into ( y = 10 - x ):", "[\ny = 10 - \frac{20}{3} = \frac{30}{3} - \frac{20}{3} = \frac{10}{3}\n]", "### Final Solution", "The solution to the system is:", "[\nx = \frac{20}{3}, \quad y = \frac{10}{3}\n]", "---", "## Why This Substitution Works", "By expressing ( y ) purely in terms of ( x ), we eliminate ( y ) from the original equation, transforming the system into one equation with a single variable. This substitution efficiently reduces complexity, aligning with best practices for solving linear systems.", "---", "## SEO Optimization Tips for This Topic", "To maximize visibility for this article, integrate relevant keywords naturally:", "- Use long-tail keywords like "how to substitute y = 10 - x in an equation" and "step-by-step substitution method for linear equations"\n- Include "solving systems of equations algebra" early to capture user intent\n- Ensure headings mirror search queries:\n - H1: How to Substitute ( y = 10 - x ) into a Linear Equation\n - H2: Step-by-Step Substitution Example\n - H3: Best Algebra Techniques for Variable Elimination\n- Embed internal links to related articles like How to Graph Linear Equations or Solving Two-Step Equations\n- Use schema markup for mathematical content (e.g., MathProofPolicy or HowTo schema) to highlight procedural clarity", "---", "## Conclusion", "Substituting ( y = 10 - x ) into a second equation is a foundational step in solving linear systems. By replacing ( y ), you simplify equations and solve efficiently using substitution. This method is not only mathematically sound but also highly valuable for students mastering algebra. Use clear explanations, step-by-step formatting, and targeted SEO techniques to help readers achieve mastery in this key skill.", "Whether you’re preparing for exams or building intuition, mastering substitution sets you free from complicated systems—one equation at a time."]