Question 882641
You can use substitution only; elimination only; or a mix of elimination and substitution.  You will have the same correct solution regardless which method you use.  


Your given system:
5x-2y=-11
3x+2y=-9
Perfectly ready for Elimination Method to start, to eliminate y.


Just sum the left members and sum the right members:
{{{5x-2y+3x+2y=-11+(-9)}}}
{{{5x+3x-2y+2y=-20}}}
{{{8x=-20}}}
{{{x=-20/8=-10/4}}}
{{{highlight(x=-5/2)}}}
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Substitute this x for either equation of the system to find the value for y.
{{{2y=-3x-9}}}
{{{y=-(3/2)x-9/2}}}
{{{y=-(3/2)*(-5/2)-9/2}}}
{{{y=15/4-18/4}}}
{{{highlight(y=-(3/4))}}}
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CHECK: Does the solution work in the original system?

5x-2y=-11

{{{5(-5/2)-2(-3/4)=-11}}}?
{{{-25/2+6/4=-11}}}
{{{-50/4+6/4=-11}}}
{{{-44/4=-11}}} TRUE.


3x+2y=-9

{{{3(-5/2)+2(-3/4)=-9}}}?
-15/2-6/4=-9
-30/4-6/4=-9
{{{-36/4=-9}}}  TRUE.


The solution really IS {{{highlight(x=-5/2)}}} AND {{{highlight(y=-3/4)}}}.


If you found disagreements about your results, check for mistakes.
(You made a sign mistake......)