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

## Expert 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 3x + 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.

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