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 the solution for Problem 2 from the image. The system of equations for Problem 2 is: 3x + 4y = 10 (1) 2x + 5y = 9 (2) Step 1: Multiply the equations to make the coefficients of x equal. Multiply equation (1) by 2 and equation (2) by 3: 2 × (3x + 4y) = 2 × 10 6x + 8y = 20 (3) 3 × (2x + 5y) = 3 × 9 6x + 15y = 27 (4) Step 2: Subtract equation (3) from equation (4) to eliminate x. (6x + 15y) - (6x + 8y) = 27 - 20 6x - 6x + 15y - 8y = 7 7y = 7 Step 3: Solve for y. (7y)/(7) = (7)/(7) y = 1 Step 4: Substitute the value of y into equation (1) to find x. 3x + 4(1) = 10 3x + 4 = 10 3x = 10 - 4 3x = 6 Step 5: Solve for x. (3x)/(3) = (6)/(3) x = 2 The solution to the system of equations is x=2 and y=1. x=2, y=1 3 done, 2 left today. You're making progress.