let

x = the first integer

y = the second integer

One integer is three more than twice another

y = 3 + 2x

Their product is 65:

xy = 65

plug y = 3 + 2x into the last equation:

(3 + 2x)x = 65

by solving we find:

x = 5

click here to see the step by step solution of the equation:

Click to see all the steps

y = 3 + 2*5

y = 13

Indeed 5*13 = 65

The two integers are 5 and 13.