x-y=3 3x-2y=3?

Question

Solve by using substitution then determine if it is independent, dependent, inconsistent

Answer 1

first move x or y to the other side of the equation. I'll move y to get x=y+3.
3(y+3)-2y=3 substitution
3y+9-2y=3 getting rid of parentheses
y=-6 simplifiaction

so, put in -6 whereever you see y and get the following
x-(-6)=3
x+6=3
x=-3

put it in the other now to see if they check out and.....
3(-3)-2(-6)=3
-9--12=3
-9+12=3 checks out, so its not inconsistent. Since there's the one and only answer, I believe that to be an independent system, but not 100% sure (been a few years since I last did H.S. math)

Answer 2

Inconsistent.

Answer 3

x-y=3

x=3+y

now subsitute this value of x in second statement

3(3+y)-2y=3

9+3y-2y=3

9+y=3

y=3-9

y=-6

now substitute this in x=3+y

x=3+(-6)

x=-3

u can substitute these value in any of the given statement and if Left hand side =right hand side, the ur answer is correct, i cheched for this, this is correct

Answer 4

x-y=3
x=3+y___equation 1
3x-2y=3__equation 2
Substituting value of x from equation 1 to equation 2
3(3+y)-2y=3
9+3y-2y=3
9+y=3
y=3-9
y=-6
Putting value of y in equation 1
x=3+(-6)
x=3-6=-3
Consistent

Answer 5

y= x-3 y = (3x-3)/2

make them equal, solve for X.

2x -6 = 3x -3
-9 = x
y = x-3 , y = -12

Answer 6

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

multiply by 3 3x-3y=9
3x-2y=3

substracting: -3y+2y=9-3
-y=6, y=-6
x=3-6=-3

answer x= -3, y= -6

Answer 7

x-y=3
i.e. 2x-2y=6
-3x-2y=3
--------------------
-x =3
x=-3
y=0

Answer 8

This might help. Just apply the same rules to your problem

http://www.public.iastate.edu/~swillson/Quadratic.pdf#search='xy%3D3%203x2y%3D3'

Answer 9

x-y=3x-2y; x=3x-y; 2x=y; x=y/2

dependent

Answer 10

3x - 2y = 3
x - y = 3
------------------
2x -y = 0
------------------
y = 2x
---------------
x - 2x = 3
x = -3
--------------
y = 2x = -6
--------------


x= -3, y= -6