Question 63883
ANSWER

How do  you solve this problem: x-3y=17
                             2x+y=17?

What is the distance formula?


ANSWER:

x - 3y = 17-----------------------------(1)


2x + y = 17------------------------------(2)



We have different methods to solve such problem.


One of them is elimination method.



For that consider equations 1 and 2



First step is to make coefficient of any of the two variable same.



here we have x and 2x.


so multiply the first equation by 2 so that the coefficient of x becomes 2.



==>  2(x - 3y )= 2*17


Remove the parenthesis,




==> 2*x - 2*3y = 34



==> 2x - 6y = 34----------------------(3)




Now consider equation (2)  and (3)





2x - 6y = 34----------------------(3)





2x + y = 17------------------------------(2)




Subtract (2) from (3){ That means subtract  left side and right side seperately)




==>2x - 6y - (2x + y) = 34 -17




==>2x - 6y - 2x - y) = 17




==>  - 7y  = 17



Divide -7 on both sides of the equation




==> - 7y/-7 = 17/7




==> y = 17/7





Now substitute this value in any one of the  given equations.



Let's take the second equation,




2x + (- 17/7 )= 17



2x - 17/7 = 17




Add 17/7 from both sides of the equation.



 
2x -17/7 + 17/7 = 17 + 17/7


2x = 136/7



Divide both sides by 2



==> 2x/2 = 136/2*7



==> x = 68/7




So the required solution is,



x = 68/7 and



y = -17/7



(You can chek this answer  by plugging these values in the given equation.)



Hope you understood.




DISTANCE FORMULA:


In algebraic geometry, one can find the distance between two points of the xy-plane using the distance formula. The distance between (x1, y1) and (x2, y2) is given by

  d = square root of { (x1 - x2)^2 + ( y1 - y2 ) ^2}


For example,


If A ( 5, 7 ) and  B( -1 , 15 )



then by distance formula, the distance betweeen A and B is given by,




d = square root of { (x1 - x2)^2 + ( y1 - y2 ) ^2}



d = square root of { (5 -  -1)^2 + ( 7 - 15 ) ^2}



d = square root of { (6)^2 + ( -8 ) ^2}



d = square root of { 36 + 64 }


d = square root of { 100 }


d = 10


That is distance between the points  A ( 5, 7 ) and  B( -1 , 15 ) is 10 units.


 

Hope you understood.



Regards,

praseenakos@yahoo.co.in