Now substitute \(x = \frac{2}{3}\) back into one of the original equations, say \(y = 2x + 3\):
["SEO-Optimized Article: How to Substitute (x = \frac{2}{3}) into the Equation (y = 2x + 3) – A Step-by-Step Guide", "Understanding how to substitute values into equations is a fundamental skill in algebra and essential for solving a wide range of mathematical problems. If you’ve recently solved for (x = \frac{2}{3}) in the equation (y = 2x + 3), this article walks you through the process clearly and provides the final result with context.", "### Why Substitute (x = \frac{2}{3}) in (y = 2x + 3)?", "Substituting a value for (x) allows us to calculate the corresponding (y)-value, helping to pinpoint a specific point on the linear function. This is especially useful in graphing, verification, or real-world modeling where precise outcomes are required.", "### The Original Equation", "Begin with the linear equation:\n[\ny = 2x + 3\n]", "### Step 1: Substitute (x = \frac{2}{3})", "Replace every instance of (x) with (\frac{2}{3}):\n[\ny = 2\left(\frac{2}{3}\right) + 3\n]", "### Step 2: Perform the Multiplication", "Multiply:\n[\n2 \ imes \frac{2}{3} = \frac{4}{3}\n]", "So:\n[\ny = \frac{4}{3} + 3\n]", "### Step 3: Add the Constants", "Convert 3 into a fraction with denominator 3:\n[\n3 = \frac{9}{3}\n]", "Now add:\n[\ny = \frac{4}{3} + \frac{9}{3} = \frac{13}{3}\n]", "### Final Result", "Substituting (x = \frac{2}{3}) into the equation (y = 2x + 3) yields:\n[\ny = \frac{13}{3}\n]", "This means when (x = \frac{2}{3}), the output value is (\frac{13}{3}), a key point on the line defined by the equation.", "### Practical Applications", "Knowing how to substitute values helps in:\n- Graphing linear equations accurately\n- Verifying calculations in physics or economics models\n- Solving real-world problems where input variables are known and output needs to be determined", "### Summary", "Substituting (x = \frac{2}{3}) into (y = 2x + 3):\n[\ny = 2\left(\frac{2}{3}\right) + 3 = \frac{13}{3}\n]", "This simple yet powerful operation bridges abstract algebra to concrete numeric results—perfect for student learners and math enthusiasts alike.", "---", "Keywords for SEO:\nsubstitute (x) in equation, solve (y = 2x + 3), algebraic substitution, linear equations, step-by-step substitution, calculate (y) from (x), math practice, verify solutions, coordinate geometry basics"]
