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
Welcome back Dr — missed you this week. To solve the system of linear equations: 1) 2x + 2y - z = -7 2) x - y + 2z = 4 3) 3x + 3y - z = 0 Step 1: Eliminate z from equations (1) and (3). Subtract equation (1) from equation (3): (3x + 3y - z) - (2x + 2y - z) = 0 - (-7) 3x - 2x + 3y - 2y - z + z = 7 x + y = 7 (*) Step 2: Eliminate z from equations (1) and (2). Multiply equation (1) by 2: 2(2x + 2y - z) = 2(-7) 4x + 4y - 2z = -14 (1') Add equation (1') to equation (2): (4x + 4y - 2z) + (x - y + 2z) = -14 + 4 4x + x + 4y - y - 2z + 2z = -10 5x + 3y = -10 (**) Step 3: Solve the system of equations () and (*) for x and y. From (*), we can express x in terms of y: x = 7 - y Substitute this into (**): 5(7 - y) + 3y = -10 35 - 5y + 3y = -10 35 - 2y = -10 -2y = -10 - 35 -2y = -45 y = (-45)/(-2) y = (45)/(2) Now substitute the value of y back into x = 7 - y: x = 7 - (45)/(2) x = (14)/(2) - (45)/(2) x = (14 - 45)/(2) x = (-31)/(2) Step 4: Substitute the values of x and y into one of the original equations to find z. Using equation (1): 2x + 2y - z = -7 2((-31)/(2)) + 2((45)/(2)) - z = -7 -31 + 45 - z = -7 14 - z = -7 -z = -7 - 14 -z = -21 z = 21 The solution is: x = -(31)/(2), y = (45)/(2), z = 21 x = -(31)/(2), y = (45)/(2), z = 21 Send me the next one 📸