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mrgoggles12
03.12.2020 •
Mathematics
True or false: An equation in the form of Ax+By=C, where A≥0, A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1 can represent either a linear or nonlinear function.
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Ответ:
x = -5, y = 31/7, and z = 30/7
Step-by-step explanation:
Step 1: Convert the system into the augmented matrix form:
•224|16
•1-23|-1
•12-3|-9
Step 2: Divide row 1 by 2 and multiply row 2 with -1 and add it into row 3:
•112|8
•1-23|-1
•04-6|-8
Step 3: Divide row 3 by 2 and multiply row 1 with -1 and add it into row 2:
•112|8
•0-3 1|-9
•02-3|-4
Step 4: Multiply row 2 with 2/3 and add it into row 3:
•112|8
•0-3 1|-9
•00-7/3|-10
Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
•x + y + 2z = 8
•-3y + z = -9
•(-7/3)z = -10 (This implies that z = 30/7.)
Step 6: Since we have calculated z = 30/7, put this value in equation 2:
•-3y + 30/7 = -9
•-3y = -93/7
•y = 31/7.
Step 7: Put z = 30/7 and y = 31/7 in equation 1:
•x + 31/7 + 2(30/7) = 8
•x = 8 - 60/7 - 31/7
•x = -5.
The mentioned options are incorrect (it can be verified by substituting all the options in the system one by one).
So final answer is x = -5, y = 31/7, and z = 30/7!!!