This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to solve the system of equations: The given system of equations is: 3x + 2y = 16 (1) x - y = 1 (2) Step 1: Solve equation (2) for y. From equation (2), we have: x - y = 1 Add y to both sides: x = 1 + y Subtract 1 from both sides to isolate y: y = x - 1 (3) Step 2: Substitute the expression for y from equation (3) into equation (1). Substitute y = x - 1 into equation (1): 3x + 2(x - 1) = 16 Step 3: Solve the resulting equation for x. Distribute the 2: 3x + 2x - 2 = 16 Combine like terms: 5x - 2 = 16 Add 2 to both sides: 5x = 16 + 2 5x = 18 Divide by 5: x = (18)/(5) x = 3.6 Step 4: Substitute the value of x back into equation (3) to find y. Substitute x = 3.6 into y = x - 1: y = 3.6 - 1 y = 2.6 The solution to the system of equations is: x = 3.6 y = 2.6