How do you solve #12y-3x=-1# and #x-4y=1# using the substitution method?

1 Answer
Dec 11, 2014

In order to solve this problem using the substitution method, we'll need to eliminate one of the variables, either #x# or #y#, in one of the equations, so that we can solve for the other.

To do that, start by isolating #x# in one of the two equations. Then, substitute the value of #x# into the other equation, and solve.


Step 1

Isolate #x# in one of the two equations. In this case, the second equation seems easier to use since I won't have to use division to isolate #x#:

#x - 4y = 1#
#x=1 + 4y#

Now we know that once we find the value of #y#, we can simply multiply it by 4 and then add 1 to find the value of #x#.

Step 2

Substitute the value of #x#, which we now know is #1 + 4y#, into the first equation:

#12y - 3x = -1#
#12y -3(1+4y)= -1#

Then, simplify it:

#12y -3(1+4y)= -1#
#12y - (3 + 12y) = -1#
#12y -3 - 12y = -1#

However, #12y# cancels, leaving:

#-3 = -1#

Since #-3 != -1#, there is no solution to this system.