Could someone please show me how to solve the system by elimination method?
5x+3y=-7 7x-2y=13

- me123

Could someone please show me how to solve the system by elimination method?
5x+3y=-7 7x-2y=13

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- anonymous

Certainly. The elimination method allows you to form a new equation with only one of your variables by adding a multiple of one equation to another.
First pick a variable you want to get rid of.

- me123

Could you show me how this is done step by step?

- anonymous

Yes, pick a variable you'd like to eliminate (x or y).

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## More answers

- me123

x

- anonymous

Ok, so checking the coefficients on x in both equations, we can see that if we multiply the first equation by \(\frac{-7}{5}\) We will have a -7 coefficient on our x term. So rewrite the first equation after multiplying it by \(\frac{-7}{5}\)

- anonymous

If anything I say doesn't make sense, stop me and let me know.

- me123

ok

- anonymous

So what do you get when you multiply the first equation by \(\frac{-7}{5}\).

- me123

do you make the 55 a fraction then cross multiply

- anonymous

No, multiply both sides of the whole equation by -7/5

- anonymous

\[\frac{-7}{5}(5x+3) = \frac{-7}{5}(-7)\]
And simplify.

- anonymous

What do you get?

- anonymous

While you're working it out I'm gonna grab some coffee.

- me123

35+3 =-49

- anonymous

You forgot to
(a) change the signs (it was a -7)
(b) put each of those over 5 (and simplify the 35)
(c) keep your x.

- anonymous

It should be:
\[\frac{-7}{5}(5x + 3y) = \frac{-7}{5}(-7)\]
\[\frac{-7}{5}(5x) + \frac{-7}{5}(3y) = \frac{49}{5}\]
\[-7x - \frac{21}{5}y = \frac{49}{5}\]

- anonymous

Right?

- me123

yes

- anonymous

Ok, now add this equation to the other one.
\(7x\ - 2y = 13\)
+ \(-7x - (21/5)y = 49/5\)
==============
For now don't bother to try to combine the fractions and non-fractions, just eliminate the x.

- me123

ok

- anonymous

What do you get for the new equation that only has y's?

- me123

13/7(7x+2y)=13/7(13)

- me123

is this step right

- anonymous

No. Just add the two equations from top to bottom:
\(7x \ - 2y \) = 13
+ \(-7x - (21/5)y = 49/5\)
===============
\(0x - 2y - (21/5)y\) = 13 + 49/5

- me123

oh ok

- anonymous

Now multiply that whole equation by 5 to get rid of the fraction

- anonymous

What do you get?

- anonymous

The equation on the bottom that only has y's that is.

- me123

so if i multiply all by 5 I get 10y -10=65+245

- anonymous

No.
5*(-2y) = -10y
5*(-21/5)y = -21y
5*13 = 65 (this part you did correctly)
5*49/5 = 49
So the equation would be -10y -21y = 65 + 49

- anonymous

Then you combine your terms.

- me123

-31y=114

- anonymous

Right, and now y =?

- anonymous

Just leave it as a fraction.

- me123

-31/114

- anonymous

Yep. Now plug that in for y into either one of your original equations and solve for x.

- anonymous

Err wait, no. It's -114/31

- anonymous

You need to practice your distribution rules, and working with equations. I suggest
http://www.khanacademy.org/video/solving-equations-with-the-distributive-property?playlist=Algebra%20I%20Worked%20Examples

- me123

thank you

- anonymous

Of course! =)

- amistre64

tag! your it

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