# solve an equation by the substitution method

#### rjohnson

##### New member
Solve this equation by the substitution method and determine whether the equations are dependent, independent or inconsistent.

3x-6y=5
2y-4x-6

#### skeeter

##### Senior Member
rjohnson said:
Solve this equation by the substitution method and determine whether the equations are dependent, independent or inconsistent.

3x-6y=5
2y-4x-6 this is not an equation, please check it.

please show what you have tried to solve this system.

also, just fyi ... I would not use substitution to solve this system.

#### rjohnson

##### New member
This problem was given to me by my algebra instructor and he wants the equation solved but I could not figure it out. Here is what I have.
3x-6y=5
2y=4x-6

6y=3x+5
3x-6y=5
3x-6y+6y=5+6y
3x=5+6y
x=5/3+6y
x=1.66+6y

2y=4(1.66+6y)-6
2y=6.66+24y-6
2y=.66+24y
y=.66/2+24y
y=.333+24y
y=1/3+24y

You said that it was not an equation. does that not make it inconsistent seeing that it cannot be solved?

#### skeeter

##### Senior Member
3x-6y=5
2y=4x-6

now that I see what the second equation is, let's do a substitution ...

first off ...
2y = 4x - 6
divide all terms by 2 ...
y = 2x - 3

now, substitute (2x - 3) for y in the first equation ...

3x - 6(2x - 3) = 5
distribute the -6 ...
3x - 12x + 18 = 5
combine like terms ...
-9x = -13
x = 13/9

go back to y = 2x - 3, substitute 13/9 for x and determine the value of y ...

y = 2(13/9) - 3 = 26/9 - 27/9 = -1/9

#### rjohnson

##### New member
Thank you

Thank you for the help. You make it seem so easy. How do you do it? I cannot seem to get a grasp of algebra.

#### jonboy

##### Full Member
Re: Thank you

rjohnson said:
Thank you for the help. You make it seem so easy. How do you do it? I cannot seem to get a grasp of algebra.
Practice. You just gotta to play around w/it and w/expirience you will learn what methods are better.