label your numbers (I'm picking x and y)
x+y=35
2x=5y
find the relationship between your numbers
x=35-y
apply this to the other equation
2 (35-y)=5y
now simplify to find y
70-2y=5y
70=7y
y=70/7=10
now apply your newly found y to find x
x+10=35
x=25
check your answers
2 (25)=5 (10)
50=50
so our first number x is 25 and our second number y is 10
