The sum of two numbers is 35. twice the first number is equal to 5 times the second number. find the two numbers

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