Question 124252
{{{-2x + 5y = -19}}}
{{{x-3y = 10}}}


Multiply the 2nd equation by 2 so that the coefficients on the x terms are additive inverses.


{{{-2x + 5y = -19}}}
{{{2x-6y = 20}}}


Now add the two equations, term-by-term, to get:


{{{0x-y=1}}}


And solve for y


{{{-y=1}}}
{{{y=-1}}}


Go back to your original two equations:
{{{-2x + 5y = -19}}}
{{{x-3y = 10}}}


Multiply the first by 3 and the second by 5:
{{{-6x + 15y =-57}}}
{{{5x-15y = 50}}}


Again, add term-by-term
{{{-x+0y=-7}}}


{{{x=7}}}


So the solution set of the system is the ordered pair (7,-1)


Check your answer:
Does the solution set make both equations true statements?

{{{-2(7) + 5(-1) = -14-5=-19}}} yes
{{{7 -3(-1) = 7 + 3 = 10}}}  yes


Further check, graph the system.  Do the graphs intersect at (7,-1)?


{{{graph(400,400,-2,8,-8,2,x/3-(10/3),(2x)/5-(19/5))}}}


Looks like it to me.