Solve the following system of linear equations: x1 + x2 - 5x3 = 8, -2x1 + 3x2 + x3 = 12, 3x1 + x2 + 4x3 = 5

Here are the steps to solve the system of linear equations: The given system of equations is: 1) x_1 + x_2 - 5x_3 = 8 2) -2x_1 + 3x_2 + x_3 = 12 3) 3x_1 + x_2 + 4x_3 = 5 Step 1: Eliminate x_1 from equations (1) and (2). Multiply equation (1) by 2: 2(x_1 + x_2 - 5x_3) = 2(8) 2x_1 + 2x_2 - 10x_3 = 16 (Equation 4) Add Equation (4) to Equation (2): (2x_1 + 2x_2 - 10x_3) + (-2x_1 + 3x_2 + x_3) = 16 + 12 5x_2 - 9x_3 = 28 (Equation 5) Step 2: Eliminate x_1 from equations (1) and (3). Multiply equation (1) by -3: -3(x_1 + x_2 - 5x_3) = -3(8) -3x_1 - 3x_2 + 15x_3 = -24 (Equation 6) Add Equation (6) to Equation (3): (-3x_1 - 3x_2 + 15x_3) + (3x_1 + x_2 + 4x_3) = -24 + 5 -2x_2 + 19x_3 = -19 (Equation 7) Step 3: Solve the system of equations (5) and (7) for x_2 and x_3. The new system is: 5) 5x_2 - 9x_3 = 28 7) -2x_2 + 19x_3 = -19 Multiply Equation (5) by 2 and Equation (7) by 5: 2(5x_2 - 9x_3) = 2(28) 10x_2 - 18x_3 = 56 (Equation 8) 5(-2x_2 + 19x_3) = 5(-19) -10x_2 + 95x_3 = -95 (Equation 9) Add Equation (8) and Equation (9): (10x_2 - 18x_3) + (-10x_2 + 95x_3) = 56 + (-95) 77x_3 = -39 x_3 = -(39)/(77) Step 4: Substitute the value of x_3 into Equation (5) to find x_2. 5x_2 - 9(-(39)/(77)) = 28 5x_2 + (351)/(77) = 28 5x_2 = 28 - (351)/(77) 5x_2 = (28 × 77 - 351)/(77) 5x_2 = (2156 - 351)/(77) 5x_2 = (1805)/(77) x_2 = (1805)/(5 × 77) x_2 = (361)/(77) Step 5: Substitute the values of x_2 and x_3 into Equation (1) to find x_1. x_1 + x_2 - 5x_3 = 8 x_1 + (361)/(77) - 5(-(39)/(77)) = 8 x_1 + (361)/(77) + (195)/(77) = 8 x_1 + (361 + 195)/(77) = 8 x_1 + (556)/(77) = 8 x_1 = 8 - (556)/(77) x_1 = (8 × 77 - 556)/(77) x_1 = (616 - 556)/(77) x_1 = (60)/(77) The solution to the system of equations is: x_1 = (60)/(77), x_2 = (361)/(77), x_3 = -(39)/(77) x_1 = (60)/(77), x_2 = (361)/(77), x_3 = -(39)/(77) Send me the next one 📸