Select ALL the correct answers.
Select all the statements that are true for the following systems of equations.
System A System B System C
2x - 3y = 4 3x - 4y = 5 2x - 3y = 4
4x - y = 18 y = 5x + 3 12x - 3y = 54
A. System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three.
B. All three systems have different solutions.
C. Systems B and C have the same solution.
D. Systems A and B have different solutions.
E. Systems A and C have the same solution.
(Select all that apply, more than one answer.)
Answers
We have been given three system of equations:
System A System B System C
2x - 3y = 4 3x - 4y = 5 2x - 3y = 4
4x - y = 18 y = 5x + 3 12x - 3y = 54
For those system of equations we have to select all the statements that are true.
A. System C simplifies to 2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three.
ANSWER:
It is TRUE because 12x-3y=54 gives 4x-y=18 after divide by 3.
B. All three systems have different solutions.
ANSWER:
FALSE, because system A and C both aer same so different solution is not possible.
C. Systems B and C have the same solution.
ANSWER:
From graph we can see that solution to system B is (-1,-2) while for system C, solution is (5,2). Both are different.
Hence statement is FALSE.
D. Systems A and B have different solutions.
ANSWER:
System A is same as system C. So A and B is like C and B. In part C) we just found that solution are different so answer is TRUE.
E. Systems A and C have the same solution.
ANSWER:
As A and C are same so yes they have same solution. Statement is TRUE
Answer:
Step-by-step explanation: