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

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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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