Substitute \( a = 1 \) and \( b = 2 \) into \( a + b + c = 6 \):

["Substituting ( a = 1 ), ( b = 2 ) into ( a + b + c = 6 ): A Beginner-Friendly Solution", "In algebra, solving equations by substituting known variables is a common and powerful technique. One straightforward application involves replacing variables ( a ) and ( b ) with specific values to simplify and solve the equation. In this article, we explore what happens when we substitute ( a = 1 ) and ( b = 2 ) into the equation:", "[\na + b + c = 6\n]", "### Step-by-Step Substitution", "1. Start with the original equation:\n [\n a + b + c = 6\n ]", "2. Substitute ( a = 1 ) and ( b = 2 ):\n [\n 1 + 2 + c = 6\n ]", "3. Simplify the left-hand side:\n [\n 3 + c = 6\n ]", "4. Solve for ( c ):\n [\n c = 6 - 3 = 3\n ]", "### Final Solution", "With substitution, we find that when ( a = 1 ) and ( b = 2 ), the value of ( c ) that satisfies the equation ( a + b + c = 6 ) is:", "[\n\boxed{c = 3}\n]", "---", "### Why This Matters in Algebra", "Substituting known values transforms a general equation into a simple linear equation in one unknown, making it easy to solve. This method is essential in solving systems of equations, optimizing expressions, and modeling real-world problems.", "Understanding how substitution works lays the foundation for more advanced topics like linear algebra, calculus, and numerical methods.", "### Key Takeaways", "- Simply replace known variable values in the equation.\n- Perform arithmetic simplifications carefully.\n- As shown, ( a = 1 ) and ( b = 2 ) yield ( c = 3 ) in ( a + b + c = 6 ).\n- Substitution is a gateway skill to deeper algebraic problem-solving.", "If you’re learning algebra or preparing for exams, practicing substitutions like this will help you master equation solving with confidence.", "---", "Keywords: substitution algebraic equations, how to substitute values, solve a + b + c = 6, variable replacement, algebra tutorial, beginner math, equation solving, c = 3, algebra basics."]