Question 41173
First thing you need to do is get both equations equal to the same thing such as x

{{{x-2y=5}}}
{{{x=2y+5}}}

Now for the other equation

{{{-3x+2y=7}}} add 3x to both sides so you will not divide by a negitive
{{{2y=3x+7}}}  subtract 7 from both sides
{{{3x=2y-7}}}  divide both sides by 3
{{{x=(2y-7)/3}}}

Now that they both equal x they can be set equal to each other because {{{x=x}}}

{{{2y+5=(2y-7)/3}}}  Multiply both sides by 3 to get rid of the fraction
{{{(2y+5)(3)=2y-7}}}
{{{6y+15=2y-7}}}  Subtract 15 from both sides
{{{6y=2y-22}}}  Subtract 2y from both sides
{{{4y=-22}}}  Divide by 4
{{{y=-5.5}}}

Now to find x you substitute the Y you just found in either of the 2 equations

{{{x-2y=5}}} substitute -5.5 for y
{{{x-2(-5.5)=5}}}
{{{x+11=5}}} Subtract 11 from both sides
{{{x=-6}}}  

So your answer is
{{{x=-6}}} & {{{y=-5.5}}}