The correct answer is:
The numbers are 14 and 16.
Explanation:
Let x and y represent the numbers. Since the sum of the numbers is 30, this gives us the equation
x+y = 30.
Since the difference of the numbers is 2, this gives us the equation
x-y = 2.
This gives us the system
[tex] \left \{ {{x+y=30} \atop {x-y=2}} \right. [/tex]
To solve this, we will eliminate one variable. Since the coefficients are all the same, but the y-variables have different signs, we will eliminate them by adding the equations together:
[tex] \left \{ {{x+y=30} \atop {+(x-y=2)}} \right.
\\
\\2x=32 [/tex]
Divide both sides by 2:
2x/2 = 32/2
x = 16.
Substitute this back into our first equation:
16+y=30
Subtract 16 from each side:
16+y-16=30-16
y=14
