Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

x

Answer 5

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 \(\frac{-7}{5}\)

Answer 6

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

Answer 7

ok

Answer 8

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

Answer 9

do you make the 55 a fraction then cross multiply

Answer 10

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

Answer 11

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

Answer 12

What do you get?

Answer 13

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

Answer 14

35+3 =-49

Answer 15

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.

Answer 16

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

Answer 17

Right?

Answer 18

yes

Answer 19

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.

Answer 20

ok

Answer 21

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

Answer 22

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

Answer 23

is this step right

Answer 24

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

Answer 25

oh ok

Answer 26

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

Answer 27

What do you get?

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

Then you combine your terms.

Answer 32

-31y=114

Answer 33

Right, and now y =?

Answer 34

Just leave it as a fraction.

Answer 35

-31/114

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

thank you

Answer 40

Of course! =)

Answer 41

tag! your it