Substitute \(x\) into the first equation: \(2(43/14) + 3y = 16\).
["Title: Solving for ( y ): Substituting ( x ) into the Equation ( 2\left(\frac{43}{14}\right) + 3y = 16 )", "Solving equations involving fractions and variables is a common task in algebra, and one practical application is substituting a known value of ( x ) into a broader equation to isolate variables like ( y ). In this article, we’ll walk through the process of substituting ( x = \frac{43}{14} ) into the equation:", "[\n2\left(\frac{43}{14}\right) + 3y = 16\n]", "and solve for ( y ), step by step. This process is useful in real-world problem solving, including finance, physics, and engineering, where variables often depend on defined parameters.", "---", "### Step 1: Simplify the Known Expression", "Start by simplifying the term involving the known value ( x = \frac{43}{14} ):", "[\n2\left(\frac{43}{14}\right) = \frac{2 \cdot 43}{14} = \frac{86}{14}\n]", "Simplify ( \frac{86}{14} ): Both numerator and denominator are divisible by 2:", "[\n\frac{86 \div 2}{14 \div 2} = \frac{43}{7}\n]", "So the equation becomes:", "[\n\frac{43}{7} + 3y = 16\n]", "---", "### Step 2: Isolate the Term with ( y )", "Subtract ( \frac{43}{7} ) from both sides to isolate ( 3y ):", "[\n3y = 16 - \frac{43}{7}\n]", "Write 16 as a fraction with denominator 7:", "[\n16 = \frac{112}{7} \quad \ ext{(since } 16 = \frac{16 \ imes 7}{7} = \frac{112}{7})\n]", "Now subtract:", "[\n3y = \frac{112}{7} - \frac{43}{7} = \frac{69}{7}\n]", "---", "### Step 3: Solve for ( y )", "Now divide both sides by 3:", "[\ny = \frac{69}{7} \div 3 = \frac{69}{7} \cdot \frac{1}{3} = \frac{69}{21}\n]", "Reduce the fraction:", "[\n\frac{69 \div 3}{21 \div 3} = \frac{23}{7}\n]", "---", "### Final Answer", "So, substituting ( x = \frac{43}{14} ) into the equation ( 2\left(\frac{43}{14}\right) + 3y = 16 ), we find:", "[\ny = \frac{23}{7}\n]", "---", "### Summary", "Substituting a known value into an equation allows you to convert a general expression into a solvable form. By simplifying step-by-step—simplifying fractions, converting decimals to fractions, subtracting, and dividing—we isolate and solve for any unknown variable efficiently. This method is essential in algebra, providing a clear path from substitution to solution.", "---", "Keywords: substitute (x), equation solving, algebra, solve for (y), fraction arithmetic, linear equation, real-world math examples", "---", "For further reading: Practice solving equations with fractions, explore variable substitution techniques, and apply algebra in practical scenarios to strengthen your problem-solving skills."]
