# [MOVED] using the substitution method to solve an equation

#### rjohnson

##### New member
Problem: Solve each system by the substitution method.

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

I have tried to solve this problem but I cannot figure out what I am doing wrong. Here is what I have done so far.

. . .x - y = 3
. . .x - y - x = 3 - x
. . .y = 3 - x

. . .3x - 2y = 3
. . .3x - 2(3 - x) = 3
. . .3x - 6 + 2x = 3
. . .5x - 6 = 3
. . .5x - 6 + 6 = 3 + 6
. . .5x = 3 + 6
. . .5x = 9
. . .x = 9/5

#### skeeter

##### Senior Member
x - y = 3
3x - 2y = 3

using the 1st equation, isolate x by adding y to both sides ...
x - y = 3
x = y + 3

substitute (y + 3) for x in the 2nd equation ...

3(y + 3) - 2y = 3

distribute ...

3y + 9 - 2y = 3

combine like terms ...

y + 9 = 3

solve for y by subtracting 9 from both sides ...

y = -6

now, go back to the equation you used for the substitution, x = y + 3.
substitute -6 for y and determine the value of x.

#### Denis

##### Senior Member
Re: useing the substitution method to solve an equation

rjohnson said:
Problem: Solve each system by the substitution method.
x-y=3 3x-2y=3
I have tried to solve this problem but I cannot figure out what I am doing wrong. Here is what I have done so far.
x-y=3
x-y-x=3-x
y=3-x
Careful Sir Johnson:
your y=3-x should be -y=3-x (or y=x-3)