Easiest method: ELIMINATION

2y - 5x = 5xy -------- eq (i)	

3y + 10x = 18xy ------ eq (ii)	

4y - 10x = 10xy	------ Multiplying eq (i ) by 2 ------- eq (iii)

7y = 28xy ---- Adding eqs (iii) & (ii)	

	

	

 ------- Substituting  for x in eq (ii)



6y + 5 = 9y ----- Multiplying by LCD, 2	

5 = 9y - 6y 

5 = 3y

 

Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
 .

2/x-5/y=5

3/x+10/y=18



find the point where they intersect?

~~~~~~~~~~~~~~~~~~~~~~~~





The way which "josgarithmetic" offers to you is wrong and without hope to get the result. 

It is because this person (I can not call him as a "tutor") is mathematically illiterate and has no any notion on

how to approach the problem correctly.





I will show you the way.





Introduce new variables u =   and  v = .

Then your system takes the form

2u -  5v =  5,    (1)
3u + 10v = 18.    (2)

Let us solve this system by the Elimination method. 
Multiply equation (1) by 2 (both sides) and then add to the equation (2).
You will get

4u + 3u = 10 + 18  --->  7u = 28  --->  u =  = 4.

Next, from (2)  10v = 18 - 3u = 18 - 3*4 = 6  --->  v =  =  = 0.6.

Now recall that u = .  Hence,  x =  = .

Similarly,  v = .  Hence,  y =  = .

The problem is solved.  The solution to the given/original system is found: x =,  y = .

The intersection point is  (x,y) = (,).
Solved.





It is a standard way solving such problems.



See the lessons 



    - Solving systems of non-linear equations in two unknowns using the Cramer's rule 



    - Solving systems of non-linear equations in three unknowns using Cramer's rule



in this site.





Also, you have this free of charge online textbook in ALGEBRA-I in this site



    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.





The referred lessons are the part of this textbook under the section "Systems of equations that are not linear".





 

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