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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.
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:
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.
So your two answers would be:
x=2 and y=1/4
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