Help to classify each system?

Question

x + y = 3
y = 2x - 3

1. Would it be no solution, one solution or infinitive solution?

2. Consistant & independent, inconsistant or consistant & dependent.

My answer is:
-one solution
-consistant & independent

But I think that it is actually no solution and inconsistant.

Thank you for your help!

Thank you so much!

Answer 1

x+y = 3
y=-x+3
y=2x-=3

Subtract them
y=2x-3
y=-x+3
0=3x-6
3x=6
x=2

x+y=3
2+y=3
y=1

So they have one solution. Not sure what you mean by question #2.

Answer 2

x + y = 3
y = 2x - 3

Solving the system by substitution gives
x + 2x - 3= 3
3x -3= 3
3x=6
x=2

y = 2(2) - 3 = 4-3 =1

The system had one solution, the ordered pair (2,1)

Consistent & independent means that a linear system has only one soultion

Inconsistent means that there are no solutions to the system

Consistent & dependent means that there are infinitely many solutions to the system.

Since this system has exactly one solution it would be classified as consistant & independent .

Answer 3

1) 3-x=2x-3 --> 3x=6 --> One solution (consistant and independent) S={(2, 1)}

Saludos.

Answer 4

Well you can solve this system

x = 3-y

y = 2*(3-y)-3 = 6-2y -3 -->y =3, x= 0

so one solution, consitent and independent.

Answer 5

y=3-x
3-x=2x-3
6-x=2x
6=3x
x=2
ONE solution (x=2, y=1)
consistant and dependent.