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.