Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the numbers.

x = 5

y = 8

Step by step solution:

The statements become the following equations.

2x + y = 18

4x - y = 12

2x + y = 18

Subtract 2x from both sides

y = - 2x + 18

Substitute into the 2nd equation

4x - (-2x + 18) = 12

4x + 2x - 18 = 12

Combine terms

6x - 18 = 12

Add 18 to both sides

6x = 30

Divide both sides by 6

x = 5

Looking back, we recall:

2x + y = 18

4x - y = 12

.

2 (5) + y = 18

10 + y = 18

Subtract 10 from both sides

y = 8

4 (5) - 8 = 12

True

So the two numbers are:

x = 5

y = 8