The system has no solution when the two equations are representing parallel lines. Parallel lines have the same slope but different y-intercepts. In this case, the given equation is 2x + 2y = 2, which can be simplified to x + y = 1.
Now, let's analyze the options:
A) 3x - 3y = 3 can be simplified to x - y = 1, which is parallel to x + y = 1. So, it's a possible equation.
B) 3x + 3y = 3 can be simplified to x + y = 1, which is the same as the given equation, so it represents the same line.
C) 2x - 2y = 2 can be simplified to x - y = 1, which is parallel to x + y = 1. So, it's a possible equation.
D) 2x + 2y = 3 cannot be simplified to x + y = 1, so it's not parallel to the given equation.
So, the possible equations that could be the other equation in the system are A) 3x - 3y = 3 and C) 2x - 2y = 2 ..
Answers & Comments
Step-by-step explanation:
The system has no solution when the two equations are representing parallel lines. Parallel lines have the same slope but different y-intercepts. In this case, the given equation is 2x + 2y = 2, which can be simplified to x + y = 1.
Now, let's analyze the options:
A) 3x - 3y = 3 can be simplified to x - y = 1, which is parallel to x + y = 1. So, it's a possible equation.
B) 3x + 3y = 3 can be simplified to x + y = 1, which is the same as the given equation, so it represents the same line.
C) 2x - 2y = 2 can be simplified to x - y = 1, which is parallel to x + y = 1. So, it's a possible equation.
D) 2x + 2y = 3 cannot be simplified to x + y = 1, so it's not parallel to the given equation.
So, the possible equations that could be the other equation in the system are A) 3x - 3y = 3 and C) 2x - 2y = 2 ..
Answer:
option (c) is the second answer