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
Step 1: Multiply the first equation by 2 and the second equation by 3 to make the coefficients of y equal. The given system of equations is: 2x - 3y = 5 (1) 3x - 2y = 20 (2) Multiply equation (1) by 2: 2(2x - 3y) = 2(5) 4x - 6y = 10 (3) Multiply equation (2) by 3: 3(3x - 2y) = 3(20) 9x - 6y = 60 (4) Step 2: Subtract equation (3) from equation (4) to eliminate y. (9x - 6y) - (4x - 6y) = 60 - 10 9x - 6y - 4x + 6y = 50 5x = 50 Step 3: Solve for x. x = (50)/(5) x = 10 Step 4: Substitute the value of x into equation (1) to solve for y. 2(10) - 3y = 5 20 - 3y = 5 Step 5: Solve for y. -3y = 5 - 20 -3y = -15 y = (-15)/(-3) y = 5 The solution to the system of equations is: x=10, y=5 Send me the next one 📸