linear equations

Question

The sum of two numbers is 8. One number is four less than twice the other. Find the numbers.

Answer 1

Since you have 2 unknown numbers equal 8, you can write x and y for the unknown numbers and write the problem as x + y = 8.

Since one number is four less than twice the other, you can write that as x = 2y - 4 (or y = 2x - 4. It doesn't make a difference in the problem or the answer): 2y = twice the other number, so 2y - 4 is four less than twice the other number. Now, since you can write x in terms of y (x = 2y - 4), you can substitute this equation for x in your original equation like so:

x + y = 8. x = 2y - 4, so

2y - 4 + y = 8. Add the y's and you now have:

3y - 4 = 8.

To find y, you need to get rid of both the 3 and the 4. Since you have 3y - 4, you need to add 4 to both sides of the equation to keep the two sides of the equation equal, so:

3y - 4 + 4 = 8 + 4

3y = 12. Now, divide both sides by 3:

3y/3 = 12/3. 3 / 3 = 1, so

1y = 4

y = 4. Now, substitute 4 for y in the original equation and solve for x:

x + y = 8

x + 4 = 8

x = 8 - 4

x = 4.

Therefore, both x and y are 4.