Question 930458

How do I solve this system using elimination? In steps please.

6/x-3/y=-4 and 9/x+9/y=21
<pre><font face = "Tohoma" size = 4 color = "indigo"><b>Let {{{x = 1/a}}}, and {{{y = 1/b}}}
Then:
{{{6/x - 3/y = - 4}}} becomes: 6a – 3b = - 4 ------- eq (i)
{{{9/x + 9/y = 21}}} becomes: 9a + 9b = 21_____3(3a + 3b) = 3(7)_____3a + 3b = 7 ---------- eq (ii)
9a = 3 --------- Adding eqs (ii) &(i)
{{{a = 3/9}}}, or {{{1/3}}}

{{{6(1/3) - 3b = - 4}}} --------- Substituting 1/3 for a in eq (i)
2 – 3b =  – 4 
– 3b = – 4 – 2 
– 3b =  – 6
{{{b = (- 6)/(- 3)}}}, or {{{2}}}

Since {{{a = 1/3}}}, then {{{1/a = 1/(1/3)}}}, or {{{3}}}
Now, since {{{x = 1/a = 3}}}, then {{{highlight_green(x = 3)}}}

Since b = 2, then {{{1/b = 1/2}}}
Now, since {{{y = 1/b = 1/2}}}, then {{{highlight_green(y = 1/2)}}}
You can do the check!! 
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