\(x = -\frac{1}{5}\) を \(y = 2x + 3\) に代入します:

["Article Title: Solving the Equation: Substituting ( x = -\frac{1}{5} ) into ( y = 2x + 3 \ – Step-by-Step Explanation", "---", "### Introduction", "Working with linear equations is a fundamental skill in algebra, essential for solving systems of equations, graphing, and real-world problem-solving. One common task is substituting a specific value of (x) into a linear equation to find the corresponding (y)-value. In this article, we explore how to substitute ( x = -\frac{1}{5} ) into the equation ( y = 2x + 3 ), demonstrating each step clearly for learners and students.", "---", "### What Does ( x = -\frac{1}{5} ) Mean?", "The value ( x = -\frac{1}{5} ) represents a precise input into algebraic expressions. Substituting this value allows us to determine the exact output (here, (y)) based on the defined relationship in the equation.", "---", "### Step-by-Step Substitution", "Given:", "[\ny = 2x + 3\n]", "Substitute ( x = -\frac{1}{5} ):", "[\ny = 2\left(-\frac{1}{5}\right) + 3\n]", "---", "#### Step 1: Multiply", "Multiply (2) by ( -\frac{1}{5} ):", "[\ny = -\frac{2}{5} + 3\n]", "---", "#### Step 2: Convert 3 to a Fraction", "To add the terms, express (3) as a fraction with denominator 5:", "[\n3 = \frac{15}{5}\n]", "Now the equation becomes:", "[\ny = -\frac{2}{5} + \frac{15}{5}\n]", "---", "#### Step 3: Add the Fractions", "Since denominators are the same, add the numerators:", "[\ny = \frac{15 - 2}{5} = \frac{13}{5}\n]", "---", "### Final Result", "[\ny = \frac{13}{5}\n]", "Thus, when ( x = -\frac{1}{5} ), the corresponding ( y )-value in the equation ( y = 2x + 3 ) is:", "[\ny = \frac{13}{5}\n]", "---", "### Why This Matters: Graphing and Real-World Applications", "Substituting values like ( x = -\frac{1}{5} ) helps plot points on a coordinate plane, crucial for graphing linear functions. This method is widely used in physics, economics, and engineering to model relationships between variables.", "---", "### Key Takeaway", "To substitute ( x = -\frac{1}{5} ) into ( y = 2x + 3 ):", "[\ny = 2\left(-\frac{1}{5}\right) + 3 = \frac{13}{5}\n]", "Understanding this substitution is the foundation for solving equations, systems, and applying algebra to real-life scenarios.", "---", "### Related Search Terms", "- How to substitute x-values into linear equations\n- Solving ( y = 2x + 3 ) step-by-step\n- How to evaluate linear functions\n- Linear equation substitution practice problems\n- Graphing ( y = 2x + 3 ) with specific x-values", "---", "Keywords: ( x = -\frac{1}{5} ), ( y = 2x + 3 ), substituting values, linear equations, algebra tutorial, solving for y, fractional algebra, mathematical substitution", "---", " meta description:\nLearn how to substitute ( x = -\frac{1}{5} ) into ( y = 2x + 3 ), step-by-step solution with fractions, perfect for algebra students and self-learners.", "---", "Published on:\n[Join your date here]\nMaster algebra with clear, detailed steps — substitute values and discover how equations work!"]