MATH SOLVE

5 months ago

Q:
# What is the solution to the following system?-4y=8 x+3y-3z=-262x-5y+z=19a) x = –53, y = –2, z = 7b) x = –41, y = –2, z = –7c) x = –11, y = –2, z = –7d) x = 1, y = –2, z = 7

Accepted Solution

A:

Answer:Option D (x = 1, y = -2, and z = 7).Step-by-step explanation:This question can be solved using multiple ways. I will use the Gauss Jordan Method.Step 1: Convert the system into the augmented matrix form:• 0 -4 0 | 8 • 1 3 -3 | -26• 2 -5 1 | 19Step 2: Divide row 1 by -4 and switch row 1 and row 2:• 1 3 -3 | -26• 0 1 0 | -2 • 2 -5 1 | 19Step 3: Multiply row 1 with -2 and add it in row 3:• 1 3 -3 | -26• 0 1 0 | -2 • 0 -11 7 | 71Step 4: Multiply row 2 with 11 and add it in row 3:• 1 3 -3 | -26• 0 1 0 | -2 • 0 0 7 | 49Step 5: Divide row 3 with 7:• 1 3 -3 | -26• 0 1 0 | -2 • 0 0 1 | 7Step 6: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:• x + 3y - 3z = -26• y = -2• z = 7Step 7: Put z = 7 and y = -2 in equation 1:• x + 3(-2) - 3(7) = -26• x - 6 - 21 = -26• x = 1.So final answer is x = 1, y = -2, and z = 7. Therefore, Option D is the correct answer!!!