Now substitute \( x = \frac{4}{3} \) back into the first equation to find \( y \):

["Certainly! Below is an SEO-optimized article about substituting ( x = \frac{4}{3} ) back into an equation to solve for ( y ), structured with clear headings, relevant keywords, and a natural flow.", "---", "# Solving for ( y ): How to Substitute ( x = \frac{4}{3} ) Back into Your Equation", "When solving equations—whether linear, quadratic, or more complex—one critical step is verifying your solution by substituting the found value back into the original equation. In this article, we’ll explore how to efficiently and accurately substitute ( x = \frac{4}{3} ) back into the first equation to determine ( y ), with practical tips to streamline your workflow.", "---", "### Why Substituting Back Matters", "After solving for ( y ), verifying your result by plugging it back into the original equation ensures your answer is correct and prevents common algebraic pitfalls. This step builds confidence in your solution and strengthens your understanding of equation behavior.", "---", "### Step-by-Step Guide to Substituting ( x = \frac{4}{3} ) into the First Equation", "Suppose your first equation is of the form:\n[\ny = f(x)\n]\nFor example, assume:\n[\ny = 2x + 7\n]\nBut let’s consider a general structure where we solve for ( y ) with a substitution of ( x = \frac{4}{3} ).", "Step 1: Begin with the original equation\nWrite down the first equation clearly. Let’s use:\n[\ny = \frac{3x - 5}{2}\n]\nThis is the equation to which we will substitute ( x = \frac{4}{3} ).", "Step 2: Perform the substitution\nReplace every occurrence of ( x ) with ( \frac{4}{3} ):\n[\ny = \frac{3\left(\frac{4}{3}\right) - 5}{2}\n]", "Step 3: Simplify step-by-step\nFirst, compute the numerator:\n[\n3 \cdot \frac{4}{3} = 4\n]\nThen subtract 5:\n[\n4 - 5 = -1\n]\nNow divide by 2:\n[\ny = \frac{-1}{2} = -\frac{1}{2}\n]", "---", "### Final Answer:\n[\n\boxed{y = -\frac{1}{2}}\n]", "---", "### Pro Tips for Smooth Substitution", "- Write carefully: Misplacing parentheses or misreading fractions can lead to incorrect values.\n- Use order of operations: Apply exponents, multiplication, and division before addition or subtraction.\n- Check arithmetic: A minor error in simplifying might change the result—review each step.", "---", "### Key Takeaways", "- Substituting ( x = \frac{4}{3} ) into the first equation lets you solve for ( y ) efficiently.\n- This method applies broadly to linear and nonlinear equations alike.\n- Always verify by returning your found ( y )-value to the original equation.", "---", "### Frequently Asked Questions (FAQ)", "Q: What does substituting ( x ) back into the equation tell me?\nA: It verifies whether your solution satisfies the original condition and confirms correctness.", "Q: Can I use this method with quadratic or exponential equations?\nA: Yes! The substitution process is identical—just follow algebra rules specific to the equation type.", "Q: What if simplifying keeps fractions?\nA: Fractions are perfectly acceptable; just reduce to simplest form when possible for clarity.", "---", "Optimize your problem-solving routine by mastering value substitution—your gateway to accurate and confident mathematical reasoning.", "---", "Keywords for SEO:\nsubstitute ( x = \frac{4}{3} ) back, solve for ( y ), verify solution, algebra substitution, direct substitution method, conditional equations, mathematical verification.", "---", "If you found this guide helpful, share it with fellow students and math enthusiasts—accuracy starts with proper steps!", "---", "Let me know if you'd like a version tailored to a specific equation type!"]