Question 822051
PUT EACH EQUATION INTO THE SAME FORM, PREFERABLY STANDARD FORM.
{{{-5x+3=6}}} and {{{x-y=4}}},
Assuming you meant:
{{{-5x+3y=6}}} and {{{x-y=4}}};
these are in the form, {{{ax+by=c}}}.


MULTIPLY ONE OR BOTH EQUATIONS SO THAT THE COEFFICIENT ON ONE OF THE VARIABLES IS THE SAME FOR BOTH EQUATIONS.
{{{-5x+3y=6}}} and {{{3(x-y)=3*4}}}, {{{3x-3y=12}}} for the second equation.


SUBTRACT (OR ADD) ONE EQUATION FROM THE OTHER.
{{{(-5x+3y)+(3x-3y)=6+12}}}
{{{-5x+3y+3x-3y=18}}}
{{{-5x+3x=18}}}
{{{-2x=18}}}


SOLVE FOR THE UN-ELIMINATED VARIABLE FIRST, AND THEN USE EITHER EQUATION TO FIND THE OTHER VARIABLE.
{{{-2x/(-2)=18/(-2)}}}
{{{x=-9}}}-----------part of the answer
'
{{{x-y=4}}}
{{{-y=4-x}}}
{{{y=x-4}}}
{{{y=-9-4}}}
{{{y=-13}}}------------------other part of answer