Question: If \( m(m + n) = 24 \) and \( m + n = 8 \), what is the value of \( m \)?
["Question: If ( m(m + n) = 24 ) and ( m + n = 8 ), what is the value of ( m )?", "---", "An Easy Algebraic Solution to a Classic Problem", "When solving equations involving two variables, substitution is often the most efficient strategy. In this case, we’re given two equations:", "1. ( m(m + n) = 24 )\n2. ( m + n = 8 )", "Rather than solving for both variables independently, we can simplify the problem using substitution—making this a straightforward algebra exercise.", "### Step 1: Use the second equation to eliminate ( n )", "From equation (2), ( m + n = 8 ), we can isolate ( n ):", "[\nn = 8 - m\n]", "### Step 2: Substitute ( n ) into the first equation", "Now, substitute ( n = 8 - m ) into equation (1):", "[\nm(m + n) = m(m + (8 - m)) = m(8)\n]", "So:", "[\nm \cdot 8 = 24\n]", "### Step 3: Solve for ( m )", "[\n8m = 24\n]", "Divide both sides by 8:", "[\nm = \frac{24}{8} = 3\n]", "---", "### Final Answer", "The value of ( m ) is 3.", "---", "Verification:", "Plug ( m = 3 ) back into the original equations:", "- ( m + n = 8 \Rightarrow 3 + n = 8 \Rightarrow n = 5 )\n- Check ( m(m + n) = 3 \cdot (3 + 5) = 3 \cdot 8 = 24 ) ✅", "The solution satisfies both conditions perfectly.", "---", "Why This Method Works", "This technique demonstrates a fundamental algebraic approach: substitution reduces complexity and isolates variables, making it ideal for problems like this where one variable is expressed in terms of another. Understanding how to manipulate and substitute equations is essential not just for math exams, but for logic and problem-solving across many STEM disciplines.", "---", "Was this helpful?\nIf you're tackling algebraic systems, remember: substitute known expressions to simplify—progress one step at a time! For more tips on solving linear equations and word problems, visit our full algebra resources [here].", "#AlgebraTips #SolveEquations #MathExplanation #WordProblems #LearnAlgebra #m(m+n)=24 #m+n=8"]
