Question 1049120
.
2/x-5/y=5
3/x+10/y=18

find the point where they intersect?
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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.


<pre>
Introduce new variables u = {{{1/x}}}  and  v = {{{1/y}}}.

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 = {{{28/4}}} = 4.

Next, from (2)  10v = 18 - 3u = 18 - 3*4 = 6  --->  v = {{{6/10}}} = {{{3/5}}} = 0.6.

Now recall that u = {{{1/x}}}.  Hence,  x = {{{1/u}}} = {{{1/4}}}.

Similarly,  v = {{{1/y}}}.  Hence,  y = {{{1/((3/5))}}} = {{{5/3}}}.

The problem is solved.  The solution to the given/original system is found: x ={{{1/4}}},  y = {{{5/3}}}.

The intersection point is  (x,y) = ({{{1/4}}},{{{5/3}}}).
</pre>Solved.


It is a standard way solving such problems.

See the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-non-linear-equations-in-two-unknowns-using-Cramer%27s-rule.lesson>Solving systems of non-linear equations in two unknowns using the Cramer's rule</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Solving-systems-of-non-linear-equations-in-three-unknowns-using-Cramer%27s-rule.lesson>Solving systems of non-linear equations in three unknowns using Cramer's rule</A>

in this site.


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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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