Question

1. the sum of two numbers is 88 and their difference is 8. set up and solve a system of equations to find the two numbers. use desmos.com to graph and solve.

let statements: let x = first number
let y = second number
equations:
solution:
interpret:

Explanation:

Step1: Define variables and set up equations

Let \( x \) be the first number and \( y \) be the second number. The sum of the two numbers is 88, so the first equation is \( x + y = 88 \). The difference of the two numbers is 8, so the second equation is \( x - y = 8 \) (assuming \( x > y \)).

Step2: Solve the system of equations

We can solve this system using the elimination method. Add the two equations together:
\[

$$\begin{align*} (x + y) + (x - y) &= 88 + 8 \\ 2x &= 96 \\ x &= \frac{96}{2} \\ x &= 48 \end{align*}$$

\]
Now substitute \( x = 48 \) into the first equation \( x + y = 88 \):
\[
48 + y = 88 \\
y = 88 - 48 \\
y = 40
\]

Answer:

Let Statements:

Let \( x \) = first number
Let \( y \) = second number

Equations:

\( x + y = 88 \)
\( x - y = 8 \)

Solution:

\( x = 48 \), \( y = 40 \)

Interpret:

The two numbers are 48 and 40, since their sum is \( 48 + 40 = 88 \) and their difference is \( 48 - 40 = 8 \), which matches the given conditions.