# How do I solve x-4y=1 and 3x+4y=7 using substitution or elimination?

*print*Print*list*Cite

### 3 Answers

You can solve it using elimination as described by the student below. It's just as easy to solve using substitution. If you're using substituition, you first need to get a variable by itself. The easiest way to do this would be to add 4y to both sides in the first equation to get x = 4y + 1. Then you're going to "substitute" this in for x in the second equation. So instead of writing 3**x** + 4y = 7, you now have 3(4y + 1) = 7. Distribute the 3 and you get 12y + 3 = 7. Subtract 3 from both sides: 12y = 4. Divide both sides by 12 to solve for y. So y = 4/12 = 1/4.

Now to solve for x, you plug in 1/4 for y into one of the equations.

3x + 4(1/4) = 7

3x + 1 = 7 Subtract 1 from both sides.

3x = 6 Divide both sides by 3

x = 2

So your solution is x = 2, y = 1/4. This can also be written as an ordered pair: (2,1/4). Notice that the same answer is found no matter whether you use substitution or elimination.

The set of equations x-4y=1 and 3x+4y=7 have to be solved.

This can be done using either substitution or elimination.

From x - 4y = 1, we get x = 1 + 4y

Substitute this for x in 3x + 4y = 7

3*(1 + 4y) + 4y = 7

3 + 12y + 4y = 7

16y = 4

y = 1/4

Now from x - 4y = 1, y can be written in terms of x as y = (x - 1)/4

Substitute for y in 3x + 4y = 7

3x + 4*(x - 1)/4 = 7

3x + x - 1 = 7

4x = 8

x = 2

The solution of the given set of equations is x = 2 and y = 1/4

Okay, so you have the two equations:

x-4y=1

3x+4y=7

Because you already have two terms that cancel out (the -4y and 4y), you will be using elimination. Simply add the two equations together.

When you do this, you should get 4x=8. Divide both sides by 4 and therefore, x=2. Choose either of the equations (I would choose the x-4y=1 because the numbers are smaller), and plug in 2 for x.

(2)-4y=1

-4y=-1

y=1/4

So your two answers would be:

x=2 and y=1/4