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've done excellent work setting up and solving this system of equations! Let's present the solution clearly. Step 1: Formulate the system of linear equations from the given information. From the first condition (5 years ago): x - 5 = 9(y - 5) x - 5 = 9y - 45 x - 9y = -45 + 5 x - 9y = -40 (1) From the second condition (10 years time): x + 10 = 3(y + 10) x + 10 = 3y + 30 x - 3y = 30 - 10 x - 3y = 20 (2) Step 2: Solve the system of equations using the elimination method. Subtract equation (2) from equation (1): (x - 9y) - (x - 3y) = -40 - 20 x - 9y - x + 3y = -60 -6y = -60 y = (-60)/(-6) y = 10 Step 3: Substitute the value of y into equation (2) to find x. x - 3y = 20 x - 3(10) = 20 x - 30 = 20 x = 20 + 30 x = 50 Step 4: State the final values for x and y. x = 50 y = 10 That's 2 down. 3 left today — send the next one.