The numbers are 10 and 15
Solution:
Let the first number be "x"
Let the second number be "y"
The difference between seven times a number and three time a second number is 25
seven times the first number - three time a second number = 25
7(x) - 3(y) = 25
7x - 3y = 25 ------ eqn 1
The sum of twice the first and five times the second is 95
twice the first number + five times the second number = 95
2(x) + 5(y) = 95
2x + 5y = 95 ------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
14x - 6y = 50 ----- eqn 3
Multiply eqn 2 by 7
14x + 35y = 665 ------- eqn 4
Subtract eqn 3 from eqn 4
14x + 35y = 665
14x - 6y = 50
( - ) --------------------
41y = 665 - 50
41y = 615
y = 15
Substitute y = 15 in eqn 2
2x + 5y = 95
2x + 5(15) = 95
2x + 75 = 95
2x = 95 - 75
2x = 20
x = 10
Thus the numbers are 10 and 15