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

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

Mathematics
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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.
Could you show me how this is done step by step?
Yes, pick a variable you'd like to eliminate (x or y).

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x
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 \(\frac{-7}{5}\)
If anything I say doesn't make sense, stop me and let me know.
ok
So what do you get when you multiply the first equation by \(\frac{-7}{5}\).
do you make the 55 a fraction then cross multiply
No, multiply both sides of the whole equation by -7/5
\[\frac{-7}{5}(5x+3) = \frac{-7}{5}(-7)\] And simplify.
What do you get?
While you're working it out I'm gonna grab some coffee.
35+3 =-49
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.
It should be: \[\frac{-7}{5}(5x + 3y) = \frac{-7}{5}(-7)\] \[\frac{-7}{5}(5x) + \frac{-7}{5}(3y) = \frac{49}{5}\] \[-7x - \frac{21}{5}y = \frac{49}{5}\]
Right?
yes
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.
ok
What do you get for the new equation that only has y's?
13/7(7x+2y)=13/7(13)
is this step right
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
oh ok
Now multiply that whole equation by 5 to get rid of the fraction
What do you get?
The equation on the bottom that only has y's that is.
so if i multiply all by 5 I get 10y -10=65+245
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
Then you combine your terms.
-31y=114
Right, and now y =?
Just leave it as a fraction.
-31/114
Yep. Now plug that in for y into either one of your original equations and solve for x.
Err wait, no. It's -114/31
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
thank you
Of course! =)
tag! your it

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