If \( x + y = 10 \) and \( x - y = 4 \), what is the value of \( 3x + 2y \)?

["### Solve for ( x ) and ( y ) Given:\nIf ( x + y = 10 ) and ( x - y = 4 ), What Is the Value of ( 3x + 2y )?", "Linear equations are a fundamental part of algebra, often appearing in math problems, standardized tests, and real-world calculations. One classic example is solving systems of equations to find unknown variables. In this article, we’ll break down how to find the values of ( x ) and ( y ) using the given equations:\n- ( x + y = 10 )\n- ( x - y = 4 )", "Once we determine ( x ) and ( y ), we’ll compute the expression ( 3x + 2y ) to answer the core question fully. Understanding how to manipulate and solve such systems not only helps with math exams but also strengthens logical thinking skills relevant in science, engineering, and finance.", "---", "### Step 1: Solve the System of Equations", "We begin with the two equations:\n1. ( x + y = 10 )  (Equation 1)\n2. ( x - y = 4 )   (Equation 2)", "To eliminate one variable and solve for the other, we can use the elimination method, which is efficient with linear equations involving sums and differences.", "Add Equation 1 and Equation 2:\n[\n(x + y) + (x - y) = 10 + 4\n]\n[\nx + y + x - y = 14\n]\n[\n2x = 14\n]\n[\nx = 7\n]", "Now that we have ( x = 7 ), substitute this value into Equation 1 to find ( y ):\n[\n7 + y = 10\n]\n[\ny = 10 - 7 = 3\n]", "---", "### Step 2: Verify the Solution", "Before using ( x = 7 ) and ( y = 3 ), verify by plugging into Equation 2:\n[\nx - y = 7 - 3 = 4\n]\nThis matches Equation 2, confirming the solution is correct.", "---", "### Step 3: Compute ( 3x + 2y )", "Now that we know:\n- ( x = 7 )\n- ( y = 3 )", "Substitute into the expression:\n[\n3x + 2y = 3(7) + 2(3) = 21 + 6 = 27\n]", "---", "### Final Answer", "The value of ( 3x + 2y ) is 27.", "---", "### Why This Matters", "Mastering systems of equations like this builds a strong mathematical foundation useful in fields such as economics, physics, computer science, and data analysis. Whether optimizing resources or analyzing cause-and-effect relationships, the ability to derive and compute unknown values efficiently is invaluable.", "---", "Key Takeaways:\n- Use the addition method to eliminate variables when dealing with ( x + y ) and ( x - y ) equations.\n- Always verify solutions by substituting back into the original equations.\n- Plugging known values into expressions like ( 3x + 2y ) completes the problem correctly.", "Learn how to solve similar equations today—your future in problem-solving starts here!", "---", "Keywords: solve linear equations, if x plus y equals 10 and x minus y equals 4, what is the value of 3x plus 2y, algebra tutorial, system of equations, elimination method, how to solve for x and y, value of 3x+2y, step-by-step math problem, high school algebra, math problem-solving, real-world math applications."]