Answer:
The system that models the situation is:
[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]
The solution is:
(9, 6)
Step-by-step explanation:
We must write the equations as indicated in the problem.
The sum of twice a number and another number is 24
a number: x
other number: y
Then
[tex]2x + y = 24[/tex]
The difference of twice the first number and the other number is 12
first number: x
other number: y
Then:
[tex]2x - y = 12[/tex]
The system that models the situation is:
[tex]\left \{{{2x + y = 24} \atop {2x - y = 12}} \right.[/tex]
To solve the system we add both equations to find the value of x
[tex]2x + y = 24\\\\2x - y = 12[/tex]
---------------------
[tex]4x +0 = 36\\\\x=\frac{36}{4}\\\\x=9[/tex]
[tex]2(9) +y = 24\\\\y=24-18\\\\y=6[/tex]
The solution is:
(9, 6)
