Question

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

Answer 1

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.

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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.