linear word problem

Question

Two numbers differ by 7. The larger number is 11 less than twice the smaller number. What are the two numbers?

Answer 1

Let x be the larger number and y the smaller number. From the description we can form two equations.

x-y = 7

2y - x = 11

Rewriting

x - y = 7

-x + 2y = 11

Adding the two equations to eliminate y:

y = 18

x - 18 = 7 --> x = 25

The larger number is 25 and the smaller number is 18