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
Your method for solving the system of equations and calculating the expression is correct. However, rounding the intermediate values for x and y to two decimal places introduces a slight error in the final answer. It's generally best to keep values as fractions until the final step to maintain accuracy. Let's re-evaluate using exact fractions: Given the system of equations: x + 2y = 10 (1) 3x - y = 5 (2) Step 1: Solve for x in terms of y from equation (1). x = 10 - 2y Step 2: Substitute this expression for x into equation (2). 3(10 - 2y) - y = 5 30 - 6y - y = 5 30 - 7y = 5 Step 3: Solve for y. 30 - 5 = 7y 25 = 7y y = (25)/(7) Step 4: Substitute the exact value of y back into the expression for x. x = 10 - 2((25)/(7)) x = 10 - (50)/(7) To combine, find a common denominator: x = (70)/(7) - (50)/(7) x = (20)/(7) Step 5: Calculate the value of 2x - 2y using the exact values of x and y. 2x - 2y = 2((20)/(7)) - 2((25)/(7)) 2x - 2y = (40)/(7) - (50)/(7) 2x - 2y = (40 - 50)/(7) 2x - 2y = (-10)/(7) As a decimal, (-10)/(7) ≈ -1.42857... Rounding to two decimal places, the value is -1.43. Your final answer of -1.42 is very close, but due to rounding y to 3.57 and x to 2.86 in intermediate steps, there's a slight difference. The more accurate value is -(10)/(7) or approximately -1.43. Last free one today — make it count tomorrow, or type /upgrade for unlimited.