SOLUTION: i'am a10TH std school girl, i'am not able to solve this particular sum in linear equations in the cross multiplication method. sum: 2(ax-by)+a+4b=0 2(bx+ay)+b-4a=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: i'am a10TH std school girl, i'am not able to solve this particular sum in linear equations in the cross multiplication method. sum: 2(ax-by)+a+4b=0 2(bx+ay)+b-4a=0      Log On


   



Question 2774: i'am a10TH std school girl, i'am not able to solve this particular sum in linear equations in the cross multiplication method.
sum:
2(ax-by)+a+4b=0
2(bx+ay)+b-4a=0

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
you have 2 variables, x and y. You need to make one variable the same in both equations then we can either add or subtract the equations to leave just the other variable.

I will make the x's the same by multiplying the first equation by b and the second equation by a:

2abx+-+2b%5E2y+%2B+ab+%2B+4b%5E2+=+0 --eqn1
2abx+%2B+2a%5E2y+%2B+ab+-+4a%5E2+=+0 --eqn2

Now, as both x-terms have the SSSSSame signs (both positive), we will SSSSSubstract, to give:

-+2b%5E2y+-+2a%5E2y+%2B+4b%5E2+%2B+4a%5E2+=+0
-2y%28a%5E2+%2B+b%5E2%29+%2B+4%28a%5E2+%2B+b%5E2%29+=+0

2y%28a%5E2+%2B+b%5E2%29+=+4%28a%5E2+%2B+b%5E2%29

2y = 4
y = 2

Now sub this into either eqn1 or eqn2. I will choose eqn1...

2abx+-+4b%5E2+%2B+ab+%2B+4b%5E2+=+0
2abx+%2B+ab+=+0
2abx+=+-ab
2x+=+-1
so x = -1/2.

jon