one number is seven less than five times another. if their sum is increased by one, the result is twelve. find the numbers

x = 8

y = 3

x = 5y - 7

x + y + 1 = 12

Because we have a value for x, we can use it in the second equation to find the value of y.

5y - 7 + y + 1 = 12

Combine like terms

6y - 6 = 12

Add 6 to both sides.

6y = 18

Divide both sides by 6.

y = 3

Now that we have a value for y we can place it back in the equation to find the value of x.

x + 3 + 1 = 12

Subtract 4 from both sides.

x = 8