Solution: Substitute $ y = 4x - 5 $ into the second equation: $ 2(4x - 5) + 3x = 10 $. Simplify: $ 8x - 10 + 3x = 10 \Rightarrow 11x = 20 \Rightarrow x = \frac{20}{11} $. Substitute back: $ y = 4\left(\frac{20}{11}\right) - 5 = \frac{80}{11} - \frac{55}{11} = \frac{25}{11} $.

["Title: How to Solve Linear Equations: Step-by-Step Substitution and Simplification Example", "---", "Understanding substitution in solving equations is a fundamental skill in algebra that simplifies complex expressions and leads to clear solutions. In this article, we’ll walk through a practical example of substituting $ y = 4x - 5 $ into a linear equation, simplifying it step-by-step, and using the result to find both $ x $ and $ y $. This methody approach not only solves the problem efficiently but also improves algebraic fluency.", "---", "### The Problem", "We are given the substitution:\n$$ y = 4x - 5 $$\nand the equation:\n$$ 2(4x - 5) + 3x = 10 $$", "---", "### Step 1: Substitute $ y = 4x - 5 $ into the equation\nSince $ y $ is already expressed in terms of $ x $, we directly replace every $ y $ in the larger equation. Here, $ y $ only appears inside parentheses, so substitution is straightforward:", "$$\n2(4x - 5) + 3x = 10\n$$", "---", "### Step 2: Simplify the expression\nNow expand the parentheses using the distributive property:", "$$\n2 \cdot 4x - 2 \cdot 5 + 3x = 10\n$$\n$$\n8x - 10 + 3x = 10\n$$", "Now combine like terms (terms with $ x $):", "$$\n(8x + 3x) - 10 = 10\n\Rightarrow 11x - 10 = 10\n$$", "---", "### Step 3: Solve for $ x $", "Add 10 to both sides:", "$$\n11x = 20\n$$", "Divide both sides by 11:", "$$\nx = \frac{20}{11}\n$$", "---", "### Step 4: Substitute $ x $ back to find $ y $", "Recall the original substitution:\n$$\ny = 4x - 5\n$$", "Substitute $ x = \frac{20}{11} $:\n$$\ny = 4\left(\frac{20}{11}\right) - 5 = \frac{80}{11} - \frac{55}{11} = \frac{25}{11}\n$$", "---", "### Final Answer", "- $ x = \frac{20}{11} $\n- $ y = \frac{25}{11} $", "---", "### Why This Method Works", "By substituting the known relationship between $ x $ and $ y $, we transformed a word problem into a simple linear equation. This process reduces complexity and eliminates variables systematically—key skills in algebra and calculus. Mastering substitution techniques empowers you to solve more advanced equations with confidence.", "---", "### Tips for Success", "- Always expand parentheses fully before combining like terms.\n- Organize terms with $ x $ on one side and constants on the other for clarity.\n- Double-check each step to avoid arithmetic errors.\n- Practicing substitution with different equations builds speed and intuition.", "---", "Master substitution and equation solving today—your algebraic foundation will grow stronger with every step!", "---", "Keywords: substitute $ y $, solve equations, simplify linear equation, substitution method, algebra example, solve for $ x $, solve for $ y $, step-by-step algebra, $ y = 4x - 5 $ application.", "---", "Meta Description:\nLearn how to substitute $ y = 4x - 5 $ into $ 2(4x - 5) + 3x = 10 $, simplify step-by-step, and find $ x = \frac{20}{11} $ and $ y = \frac{25}{11} $. Master substitution for clearer, faster algebra."]