The sum of two numbers is twenty four. the second number is six less than the first. write a system of equations and solve it to find the number

Step-by-step explanation:

In these types of algebra problems where we are given numbers that are "unknown" and asked to find them, it is a good idea to give them names.

Let the larger number be X.

Let the smaller number be Y.

If the larger number is three times the smaller number, we can use this information to write an equation, using our labels for the two unknown numbers. See how I translate this sentence into an equation:

The larger number is three times the smaller number.

                    X           =     3     *               Y

X = 3*Y

We've got one equation down. Since we have two variables, we're going to need two equations to solve for both of them.

The sum of two numbers is twenty-four.

                      X    +    Y    =     24

X+Y = 24

But, from our previous equation, we know that X is the same as 3*Y. This allows us to substitute "X" with "3*Y" in our second equation since the two are equal according to the first equation.

(3*Y) + Y = 24.

3Y + Y = 24

4Y = 24

4Y / 4 = 24/4

Y = 6

Now we've got the value of the smaller number. Let's plug it into our first equation,

X = 3*Y.

X = 3*(6)

X = 18

We can check our work by plugging both values into both equations and seeing if they work out:

6+18 = 24  

6*3 = 18

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81

8.75

how-to:

first, we need to find what we have to work with.

since i know that we have 7 (years) and 0.8 (inches), we can use these to solve and find the equation!

secondly, what you want to do, is see that we need to know how much growth out of the 0.8 inches he got in only 1 year, instead of 7 years.

let's try to divide.

7 ÷ 0.8 = 8.75