Solution: Solve the system: From $ x - y = 1 $, express $ x = y + 1 $. Substitute into the first equation: $ 3(y + 1) + 2y = 6 \Rightarrow 3y + 3 + 2y = 6 \Rightarrow 5y = 3 \Rightarrow y = \frac{3}{5} $. Then $ x = \frac{3}{5} + 1 = \frac{8}{5} $. \boxed{\dfrac{8}{5}}

["# Solve Linear Systems: A Step-by-Step Guide to Find Exact Solutions", "Understanding how to solve systems of linear equations is a fundamental skill in algebra and applied mathematics. Whether you're balancing budgets, analyzing scientific data, or programming algorithms, knowing how to systematically solve equations ensures accuracy and clarity. This article walks you through a classic linear system using substitution—showing how substitution simplifies complex equations into manageable solutions.", "## The System to Solve", "We begin with two equations:\n1. ( x - y = 1 )\n2. ( 3x + 2y = 6 )", "At first glance, solving two variables seemingly requires more than one step. However, by leveraging substitution—a powerful algebraic technique—we can isolate one variable and substitute its expression into the second equation, reducing complexity and uncovering precise values for ( x ) and ( y ).", "## Step 1: Express One Variable in Terms of the Other", "From the first equation ( x - y = 1 ), isolate ( x ) to simplify substitution:\n[\nx = y + 1\n]\nThis simple rearrangement transforms the system, replacing ( x ) in the second equation with ( y + 1 ).", "## Step 2: Substitute into the Second Equation", "Now substitute ( x = y + 1 ) into the second equation:\n[\n3x + 2y = 6\n]\nBecoming:\n[\n3(y + 1) + 2y = 6\n]", "## Step 3: Simplify and Solve for ( y )", "Expand and combine like terms:\n[\n3y + 3 + 2y = 6\n]\n[\n5y + 3 = 6\n]\nSubtract 3 from both sides:\n[\n5y = 3\n]\nDivide by 5:\n[\ny = \frac{3}{5}\n]", "## Step 4: Back-Substitute to Find ( x )", "Now that ( y ) is known, use ( x = y + 1 ) to find ( x ):\n[\nx = \frac{3}{5} + 1 = \frac{3}{5} + \frac{5}{5} = \frac{8}{5}\n]", "## Final Solution", "The solution to the system is:\n- ( x = \dfrac{8}{5} )\n- ( y = \dfrac{3}{5} )", "Expressed concisely:\n[\n\boxed{\dfrac{8}{5}}\n]", "## Why This Method Works", "The substitution technique excels in simplifying complex systems by reducing two variables to one, turning abstract equations into tangible values. It’s a foundational tool used in engineering, economics, and computer science—proving that even sophisticated problems yield clear answers with careful, logical steps.", "By mastering such methods, you empower yourself to tackle any linear system with confidence—essential for both academic success and real-world problem-solving."]