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

Asked on by cbrown00

sasma | High School Teacher | (Level 1) Adjunct Educator

Posted on

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.

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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

smarthottie | Student, Grade 10 | eNotes Newbie

Posted on

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