How do you solve 12y-3x=-112y3x=1 and x-4y=1x4y=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 xx or yy, in one of the equations, so that we can solve for the other.

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


Step 1

Isolate xx 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 xx:

x - 4y = 1x4y=1
x=1 + 4yx=1+4y

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

Step 2

Substitute the value of xx, which we now know is 1 + 4y1+4y, into the first equation:

12y - 3x = -112y3x=1
12y -3(1+4y)= -112y3(1+4y)=1

Then, simplify it:

12y -3(1+4y)= -112y3(1+4y)=1
12y - (3 + 12y) = -112y(3+12y)=1
12y -3 - 12y = -112y312y=1

However, 12y12y cancels, leaving:

-3 = -13=1

Since -3 != -131, there is no solution to this system.