The numbers are 10 and 3.
Step-by-step explanation:
STEP 1: Based on the problem, two equations can be set up:
First, "one number is seven less than another." This can be expressed mathematically:
Let x = first number
y = second number
[tex]x \ - 7 = \ y[/tex]
The second equation is based on "their sum is thirteen."
[tex]x \ + \ y \ = 13[/tex]
STEP 2: Solve for the variables.
In this step, substitute the value of y from Equation 1 into Equation 2:
[tex]x \ + \ (x \ - \ 7) \ = \ 13\\2x \ - \ 7 \ = 13\\[/tex]
Next, solve for x by manipulating the equation:
[tex]2x \ = \ 13 \ + \ 7\\2x \ = \ 20\\\boxed {x \ = \ 10}[/tex]
Now that the value of x is known, it can be used to determine the value of y.
To do this, use the calculated value for x and plug it into Equation 1:
[tex]y \ = \ x \ - 7\\y \ = 10 \ - 7\\\boxed {y = \ 3}[/tex]
Learn More
Keywords: two equations, two variables
