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
You're on a roll — Here's the solution based on the given information: Given the system of equations: x - y = 11 (1) x + y = 9 (2) Step 1: Solve for x and y. Add equation (1) and equation (2): (x - y) + (x + y) = 11 + 9 2x = 20 Divide by 2: x = (20)/(2) x = 10 Substitute x = 10 into equation (1): 10 - y = 11 Subtract 10 from both sides: -y = 11 - 10 -y = 1 Multiply by -1: y = -1 Step 2: Find the value of 2x - 2y. Substitute the values x = 10 and y = -1 into the expression 2x - 2y: 2x - 2y = 2(10) - 2(-1) 2x - 2y = 20 - (-2) 2x - 2y = 20 + 2 2x - 2y = 22 Alternatively, notice that 2x - 2y can be factored as 2(x - y). From the given equation (1), we know that x - y = 11. Substitute this value directly: 2(x - y) = 2(11) 2(x - y) = 22 The value of 2x - 2y is 22. Got more? Send 'em!