\(x = \frac{27}{11}\) を \(y = 3x - 5\) に代入します：

["# Substituting ( x = \frac{27}{11} ) into ( y = 3x - 5 ): A Step-by-Step Explanation", "Understanding how to substitute a value into a linear equation is a fundamental skill in algebra. In this article, we’ll walk through the process of substituting ( x = \frac{27}{11} ) into the linear equation ( y = 3x - 5 ), explaining each step clearly and confirming the correct mathematical approach.", "## What Does Substitution Mean?", "When we substitute a value into an equation, we simply replace the variable with the given number, treating that number as the variable’s value. For the equation ( y = 3x - 5 ), substituting ( x = \frac{27}{11} ) means we replace every instance of ( x ) with ( \frac{27}{11} ). This allows us to compute the corresponding ( y )-value efficiently.", "## The Substitution Process", "Start with the original equation:", "[\ny = 3x - 5\n]", "Replace ( x ) with ( \frac{27}{11} ):", "[\ny = 3 \left( \frac{27}{11} \right) - 5\n]", "Now simplify step by step:", "First, multiply:\n[\n3 \ imes \frac{27}{11} = \frac{81}{11}\n]", "So:\n[\ny = \frac{81}{11} - 5\n]", "To subtract, express ( 5 ) as a fraction with denominator 11:\n[\n5 = \frac{55}{11}\n]", "Now perform the subtraction:\n[\ny = \frac{81 - 55}{11} = \frac{26}{11}\n]", "## Final Result", "After substitution and simplification, the value of ( y ) is:", "[\n\boxed{y = \frac{26}{11}}\n]", "This result proves that when ( x = \frac{27}{11} ), the corresponding ( y )-value on the line defined by ( y = 3x - 5 ) is ( \frac{26}{11} ).", "Using this method, students and math learners can confidently evaluate linear functions and deepen their understanding of substitution—the building block for more advanced algebra.", "---", "### Why This Matters in Algebra", "Linear equations model relationships between variables frequently in science, economics, and engineering. Mastering substitution enables you to analyze graphs, solve for unknowns, and apply equations to real-world problems efficiently.", "In summary, substituting ( x = \frac{27}{11} ) into ( y = 3x - 5 ) is straightforward and yields ( y = \frac{26}{11} ), illustrating key algebraic reasoning in one clear calculation."]