Sustituye en \( 4x - y = 5 \): \( 4 \times \frac{11}{7} - y = 5 \).

["Title: How to Solve ( 4x - y = 5 ) by Substituting ( 4 \ imes \frac{11}{7} - y = 5 ): A Step-by-Step Guide", "If you’ve encountered the equation ( 4x - y = 5 ) and found yourself tasked with solving for ( y ) in terms of substituted values, you’re in the right place. In this article, we’ll explore how to transform the original equation by substituting the expression ( 4 \ imes \frac{11}{7} ) for part of the expression, making it easier to isolate ( y ) and solve the linear system. This approach is especially useful when practicing substitution in algebra, particularly in word problems or real-world applications involving linear relationships.", "---", "### Understanding the Equation: ( 4x - y = 5 )", "The equation ( 4x - y = 5 ) represents a linear relationship between variables ( x ) and ( y ). Often, such equations appear in systems of equations, optimization problems, or when modeling costs and revenue. Solving for one variable in terms of the other allows us to express ( y ) as a function of ( x ), or vice versa.", "---", "### Substitution: What Does ( 4 \ imes \frac{11}{7} - y = 5 ) Mean?", "The expression ( 4 \ imes \frac{11}{7} - y = 5 ) suggests substituting the value of ( 4 \ imes \frac{11}{7} ) into the original equation. Let’s clarify this step clearly:", "- First, compute ( 4 \ imes \frac{11}{7} ):\n [\n 4 \ imes \frac{11}{7} = \frac{44}{7}\n ]", "- Now substitute into the equation:\n [\n \frac{44}{7} - y = 5\n ]", "This substitution effectively eliminates ( y ) from the substituted side and simplifies solving for ( y ) directly.", "---", "### Step-by-Step Substitution and Solving", "Here’s how to complete the substitution and solve for ( y ):", "1. Substitute the computed value:\n Replace ( 4x ) with ( \frac{44}{7} ) (since ( x = \frac{11}{7} ) implies ( 4x = \frac{44}{7} )):\n [\n \frac{44}{7} - y = 5\n ]", "2. Isolate ( y ):\n Subtract ( \frac{44}{7} ) from both sides:\n [\n -y = 5 - \frac{44}{7}\n ]", "3. Convert 5 to a fraction with denominator 7:\n [\n 5 = \frac{35}{7}\n ]", "So,\n [\n -y = \frac{35}{7} - \frac{44}{7} = \frac{35 - 44}{7} = \frac{-9}{7}\n ]", "4. Multiply both sides by -1 to solve for ( y ):\n [\n y = \frac{9}{7}\n ]", "---", "### Why This Substitution Method Works", "Substituting known values into the original equation reduces complexity, especially when dealing with fractions or decimals. By simplifying one side first, you convert the equation from a system into a single-variable equation, which is straightforward to solve.", "This technique is valuable when:\n- You’re solving for a variable in applied contexts (construction costs, wage computations, etc.)\n- You’re analyzing linear relationships graphically\n- You prepare for more complex methods like elimination or matrix solving", "---", "### Final Answer", "From the substitution ( 4 \ imes \frac{11}{7} - y = 5 ), solving for ( y ) gives:\n[\ny = \frac{9}{7}\n]", "---", "### Key Takeaways", "- Substitute known values to simplify equations involving variables.\n- Always compute expression values before replacing variables.\n- Isolating the variable step-by-step ensures accuracy.\n- This method supports understanding linear systems and real-world problem solving.", "Keywords: solve linear equations, substitution method, algebra practice, ( 4x - y = 5 ), solving for ( y ), fractions in algebra, step-by-step solution, linear equations with fractions.", "---", "Explore more algebra techniques and apply substitution daily to build confidence in solving equations efficiently!"]