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

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

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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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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

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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

 

So your two answers would be:

x=2 and y=1/4

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