The sum of two numbers is 21 five times the first number added to 2 times the second number is 66 find the two numbers

Label your unknown numbers

I'm calling them x and y

x+y=21

5x+2y=66

find a relation of x and y

y=21-x

substitute this into your second equation

5x+2 (21-x) = 66

simplify to find x

5x+42-2x=66

3x+42=66

3x=24

x=24/3=8

apply your findings to find the second number

8+y=21

y=13

check your answer

5 (8) + 2 (13) = 66

40+26=66

we now know that the first number x is 8

and the second number y is 13