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

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 $x$:

$x - 4 y = 1$
$x = 1 + 4 y$

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 $1 + 4 y$, into the first equation:

$12 y - 3 x = - 1$
$12 y - 3 \left(1 + 4 y\right) = - 1$

Then, simplify it:

$12 y - 3 \left(1 + 4 y\right) = - 1$
$12 y - \left(3 + 12 y\right) = - 1$
$12 y - 3 - 12 y = - 1$

However, $12 y$ cancels, leaving:

$- 3 = - 1$

Since $- 3 \ne - 1$, there is no solution to this system.