Question 213715
{{{6x-5y=-3}}}
{{{2y-9x=-1}}}


Step 1.  Rearrange to align the x and y terms.


{{{6x-5y=-3}}}  multiply by 3  to both sides to get 18x
{{{-9x+2y=-1}}}  multiply by 2 to both sides to get -18x


{{{18x-15y=-9}}}   Eq 1
{{{-18x+4y=-2}}}   Eq 2


Step 2.  Adding above equations Eq 1 and Eq 2 yields


{{{-11y=-11}}} or y=1


Step 3.  Substitute y=1 into 6x-5y=-3 yields


{{{6x-5(1)=-3}}}


{{{6x=-3+5}}}


{{{6x/6=2/6}}}


{{{x=1/3}}}


Step 4.  The solution is {{{x=1/3}}} and {{{y=1}}}.


Step 5.  To verify, the following will solve the linear systems using substitution.


*[invoke linear_substitution "x", "y", 6, -5, -3, -9, 2, -1 ]


Step 6.  Same result...the solution is {{{x=1/3}}} and {{{y=1}}}.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J