Answer:
Part 1) Is a consistent independent system, because has exactly one solution.
Part 2) Is a inconsistent system, because has no solution.
Step-by-step explanation:
Part 1) we have
we have
[tex]-x=3-y[/tex]
isolate the variable y
[tex]y=x+3[/tex] -----> equation A
[tex]-7+y=-x-2[/tex]
isolate the variable y
[tex]y=-x-2+7[/tex]
[tex]y=-x+5[/tex] ----> equation B
Solve the system by elimination
Adds equation A and equation B
[tex]y=x+3\\y=-x+5\\---------\\y+y=3+5\\2y=8\\y=4[/tex]
Find the value of x
substitute the value of y in equation A or equation B
[tex]4=x+3\\x=1[/tex]
The solution is the point (1,4)
therefore
Is a consistent independent system, because has exactly one solution.
Part 2) we have
we have
[tex]x=3-y[/tex]
isolate the variable y
[tex]y=-x+3[/tex] -----> equation A
[tex]-7+y=-x-2[/tex]
isolate the variable y
[tex]y=-x-2+7[/tex]
[tex]y=-x+5[/tex] ----> equation B
Compare equation A and equation B
Line A and Line B have the same slope (m=-1) and different y-intercept
so
Line A and Line B are different parallel lines
The system has no solution
therefore
Is a inconsistent system, because has no solution.
