5x+6y=6 and 9x+9y=9 what is x and what is y

That's the question I thought you might ask !!!

We're trying to "match" terms so that, when we subtract one equation from the other, a variable "disappears."

Note that we could have mutiplied x + y = 1 by 6 on both sides giving 6x + 6y = 6

And, if  I  subtracted this from 5x + 6y = 6  notice that the "y's" would have disappeared, thusly

  5x + 6y = 6    ⇒    5x  + 6y  =  6

-[6x + 6y = 6]  ⇒   - 6x -  6y  = -6

----------------         ----------------

                              -1x         =   0            so ... x = 0  

And we could have found "y" by substituting 0 in for "x"  into the equation x + y = 1.....we would then find that y =1  ....just like before !!

This is an topic in Algebra (I don't know if you've encountered that or not)...so, if you haven't, don't worry about it too much....!!

y=1 x=0

The way we get this is called solving by elimination.  First take the equations with the nines and divide both sides by 9, this produces x+y=1.  We then multiply this by five to get 5x+5y=5.  Subtracting this from the fist equation gives us y=1.  By substituting y=1 back into either equation we get our value for x.  For example:

y+x=1

1+x=1

x=0

Nice explanation, jboy314.....3 points and a thumbs-up from me.....

BTW...welcome to the forum....I don't believe I've seen you here before.....

jboy314 pls can u show its working becoz i think i may understand much nicely then !btw u explained it really very nicely but i am still unable to get it maybe becoz i have the habbit of seeing the working !lol! CPhill i saw jboy314 before answering really very good to some questions!so jboy314 if u dont mind pls can u show me the working !

Here's what jboy314 did, rosala

He took this equation ..... 9x + 9y = 9     and divided every term by 9.....so we have

9x/9  +  9y/9   = 9/9      and this gives us  

x + y  = 1       then, he multiplied every term by 5 ..(the reason for this will be clear in a second).. so we have

5x + 5y  = 1     Notice carefully, what happens if I take this equation and subtract it from  5x + 6y =6, we have:

         5x + 6y  = 6       ⇒    5x   + 6y  =  6   

-      (5x + 5y  = 5)      ⇒   -5x   -  5y  = -5

-----------------------           -----------------

                                                     y  =  1       

( Notice how the 5x terms cancelled each other !!!! That's why it's called the "elimination" method...jboy314  saw that he could eliminate  "x"  by multiplying x + y = 1 by 5 and then subtracting it from the other equation !!!! )

Now, all we need to do is to substitute  1 for y in any of the equations to find "x"...using x + y = 1 is easiest..so we have

x + (1) = 1      subtract 1 from both sides

   -   1  = -1

---------------

x         =   0

So  x = 0    and   y =1   are our solutions  !!!

CPhill ive undertood the method and how u got the answer but still i have one  doubt left , its that how do we know that we have to multiply every term by 5 to get the answer??!!

Thanks for jumping in and cleaning up what i left behind the curtain so to speak.  Good thread!

Actually, jboy314, you didn't leave much unsaid....the 'elimination" method is easy to use, but the "strategy" behind it is hard to explain  !!!

Thank u CPhill!thumbs up for the explaination!