Question 936776
Solve for x & y. 2/x-3/y=-5  4/x+6/y=14  Thanks for your help.
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{{{2/x - 3/y = - 5}}} ------- eq (i)
{{{4/x + 6/y = 14}}} ------- eq (ii)
Let {{{a = 1/x}}}, and {{{b = 1/y}}}
Then {{{2/x - 3/y = - 5}}} becomes: 2a – 3b = - 5 ------ eq (iii)
Also, {{{4/x + 6/y = 14}}} becomes: 4a + 6b = 14 ------- eq (iv)
4a – 6b = - 10 -------- Multiplying eq (iii) by 2 ----- eq (v)
8a = 4 ------- Adding eqs (v) & (iv)
a = {{{4/8}}}, or {{{1/2}}} 

{{{2(1/2) - 3b = - 5}}} -------- Substituting ½ for a in eq (iii) 
1 – 3b = - 5 
– 3b = - 5 – 1 
– 3b = - 6
b = {{{(- 6)/(- 3)}}}, or 2

Since {{{system(a = (1/2)_and,a = 1/x)}}}, then {{{1/2 = 1/x}}}
{{{x = 2}}} ------ Cross-multiplying

Since {{{system(b = 2_and,b = 1/y)}}}, then {{{2 = 1/y}}}
2y = 1 ------ Cross-multiplying
{{{y = 1/2}}}

{{{highlight_green(system(x = 2_and,y = 1/2))}}}