Find the numbers whose sum is 9 if three times the first num

Find the numbers whose sum is 9, if three times the first number increased by two times the second equals 22.

Solution

This is a typical system equations problem. First declaration related two numbers: X and Y by adding :

X + Y = 9 (1)

Next, both number are related again but we can read: \"three times the first number\", means: 3X, in the same way, \"two times the second: 2Y. The increment can be interpreted by mean:

3X + 2Y = 22 (2)

We can see that we have two equations and two variables. We can solve this system to find the values of the two numbers: X and Y, like this:

1) solve X from de equation 1: X = 9 - Y (3)

2) replace this in equation 2:

3(9-Y) + 2Y = 22 ---> 27 - 3Y + 2Y = 22 ---> - Y = 22 - 27 ---> Y = 25.

3) now we can get the X value replace the Y value in the equation 3, so

X = 9 - 25 = -16

finally we found the solution: X = -16 and Y = 25