## Simultaneous equations using the elimination method

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
bob123
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### Simultaneous equations using the elimination method

I started with the equations y=1/4x +7, y=-3/5x - 4. I then made the number the subject and got -7=1/4x-y, 4=-3/5x-y.
What do i do from there. If you dont want to give the direct answer then dont worry. Just an example like that question will be fine.
~bob123~

jg.allinsymbols
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Joined: Sat Dec 29, 2012 2:42 am
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### Re: Simultaneous equations using the elimination method

The form in which you want to use your equations is often your choice, but your notation needs improvement. One would assume you are dealing with linear equations as found in beginning and intermediate algebra. YOUR given equations are probably these:

y=(1/4)x +7, y=-(3/5)x - 4, using parentheses for clarity.

You could arrange the equations so the variable terms come first, and the constant terms are on the other side of equality.

(1/4)x-y=7
AND
-(3/5)x-y=4

Or, better,

(1/4)x-y=7
AND
(3/5)x+y=-4

Better comfort in solving if we clear away the fractions. Multiply the "7" equation by 4 and multiply the "-4" equation by 5 to get:

A Good System Now:
----------------------------
x-4y=28
AND
3x+5y=-20
-----------------------------

You wanted to solve by elimination. First, we can multiply the first equation by 5, and multiply the second equation by 4. This will allow us to eliminate terms of y and solve for x:

5(x-4y)=5*28
and
4(3x+5y)=4*(-20)

5x-20y=140
and
12x+20y=-80

We ADD those two resulting equations giving us this:
5x-20y+12x+20y=140+(-80)
17x=60
x=60/17, ONE RESULT FOUND.

Now we can do similarly to eliminate x. We start again from here:
x-4y=28
AND
3x+5y=-20

Multiply the first equation by 3, and then subtract one equation from the other.
3x-12y=84
AND
3x+5y=-20
Try subtracting first from the second:
3x+5y-3x--12y=-20-84
5y+12y=-104
17y=-104
y=-104/17, OUR OTHER RESULT FOUND