subtract the 1st equation from the 2nd.
now, subtract 2 from both sides to isolate x
-2=x or x=-2
now plug that into either of the original equations
such as y=2x+3
giving y=2(-2)+3 =-4+3=-1
x=-2, and y=-1
the solution (x,y) is (-2,-1)
check the answer by plugging that solution into the other equation y=3x+5 =3(-2)+5=-6+5=-1. it works. y=-1
another way to solve this is graph both equations, and find where they intersect. The intersection point will be the point (-2,-1)
Graph of 1st has y-intercept of 3 and slope 2. 2nd has y-intercept of 5 and slope 5. Even a very rough sketch of the graph shows an intersection where both x and y are negative. A careful sketch gives you the answer.