2(3) + y(-2) + (-1)(y) = 6 - 2y - y = 6 - 3y = 0.

["Solving the Equation 2(3) + y(−2) + (−1)(y) = 6 − 2y − y = 6 − 3y = 0: A Step-by-Step Guide", "Learning how to solve linear equations is fundamental in algebra, and mastering expressions like 2(3) + y(−2) + (−1)(y) = 6 − 2y − y = 6 − 3y = 0 helps build strong problem-solving skills. In this article, we’ll break down how to solve this equation step-by-step, simplify expressions involving y, and arrive at the solution clearly.", "---", "### Understanding the Equation", "We start with:", "2(3) + y(−2) + (−1)(y) = 6 − 2y − y = 6 − 3y = 0", "Let’s simplify both sides carefully. The left-hand side involves multiplication terms and the variable y, while the right-hand side is a constant.", "---", "### Step 1: Simplify Left-Hand Side", "- Calculate 2(3) = 6\n- Rewrite y(−2) as -2y\n- Rewrite (−1)(y) as -y", "Now substitute:", "6 − 2y − y", "Combine like terms:\n−2y − y = −3y", "So the left-hand side simplifies to:\n6 − 3y", "Now the equation reads:\n6 − 3y = 6 − 3y", "---", "### Step 2: Analyze the Simplified Equation", "We now have:", "6 − 3y = 6 − 3y", "This is actually an identity — both sides are identical. This means the equation holds true for all real values of y, because no matter what y is, both sides are equal.", "To confirm:", "Subtract 6 from both sides:\n−3y = −3y", "Add 3y to both sides:\n0 = 0 — always true", "---", "### Step 3: Solve for y (or Recognize No Unique Solution)", "Although the equation simplifies to an identity, this does not mean there’s no solution. Instead, it means every real number is a solution — the equation is true for all y.", "However, if this equation arose as part of a broader problem, you’d typically end by stating:", "> The equation has infinitely many solutions: any real number value of y satisfies it.", "If you’re working alone and want to “solve for y,” note that the equation reduces to:", "6 − 3y = 6 − 3y\nSubtract 6:\n−3y = −3y\nAdd 3y:\n0 = 0", "This confirms the equation is always true — no specific value for y satisfies it uniquely — instead, all real values of y are solutions.", "---", "### Step 4: Verifying the Original Form", "Recall the original expression:\n2(3) + y(−2) + (−1)(y) = 6 − 2y − y = 6 − 3y = 0", "We simplified correctly from:\n6 − 3y = 0, a corrected target?", "Wait — wait a minute. The final simplified form 6 − 3y = 0 (not 6 − 3y = 6) appears to be corrected or misstated in prior steps.", "Let’s recheck:", "- Original left side: 2(3) − 2y − y = 6 − 3y\n- Right side: 6 − 2y − y = 6 − 3y\n- So equation: 6 − 3y = 6 − 3y", "But in the prompt, the equation is written as:", "2(3) + y(−2) + (−1)(y) = 6 − 2y − y = 6 − 3y = 0", "So the equation ends at 6 − 3y = 0, not 6 − 3y = 6. Therefore, the correct simplification is:", "6 − 3y = 0", "---", "### Step 5: Solve Corrected Equation: 6 − 3y = 0", "Now solve for y:", "6 − 3y = 0", "Subtract 6:\n−3y = −6", "Divide both sides by −3:\ny = 2", "---", "### Final Answer: Solving the Equation Correctly", "Understood from the original prompt’s notation, the expression:", "2(3) + y(−2) + (−1)(y) = 6 − 2y − y\n=>\n6 − 2y − y = 6 − 3y = 0\n=>\nFinal simplified:\n6 − 3y = 0\n=>\ny = 2", "⚠️ Important Clarification:\nEarlier simplification to 6 − 3y = 6 was incorrect as per the original equation’s right-hand side. The equation equals 0, not 6. Correctly, 6 − 3y = 0 yields y = 2.", "---", "### Why This Matters", "Misreading equations is common. In algebra, correctly identifying constants and combining like terms is key. Recognizing identities versus equations prevents solving failures.", "Use this guide next time you encounter expressions involving linear combinations of y — always simplify carefully, check constants, and remember:", "- If both sides reduce to the same expression: infinite solutions.\n- If sides differ: no solution.\n- If leads to 0 = 0: all real numbers are solutions.", "But always verify the original equation — sometimes formatting errors lead to confusion.", "---", "### Summary", "- Original: 2(3) + y(−2) + (−1)(y) = 6 − 2y − y\n- Simplifies correctly to: 6 − 3y = 0\n- Solution: y = 2\n- The expression equals zero, not 6\n- Avoid mistaking identity for equation — confirm RHS carefully", "---", "### Key Takeaways for SEO", "- Use natural, conversational phrasing optimized for users searching “solve 2(3) + y(−2) + (−1)(y) = 6 − 2y − y”\n- Include targeting long-tail keywords like “solve linear equation with y” and “how to simplify y expressions”\n- Clearly separate simplification steps to aid readability and SEO\n- Explain why incorrect assumptions (like 6−3y=6) lead to errors\n- Highlight the correct path: 6−3y=0 → y=2 — making it a trustworthy, educational resource", "---", "## Final Answer Recap", "[\n\boxed{y = 2}\n]"]