Answer:
Infinitely many solutions.
Step-by-step explanation:
Systems of equations can be solved through substitution, elimination, or graphing. For this problem, let's solve the system through substitution.
Given the system of equations:
[tex]x-2y=8[/tex]
[tex]3x-6y=24[/tex]
Focusing on the first given equation, we can solve for the x-variable by adding the term "2y" to both sides of the equation:
[tex]x= 2y+8[/tex]
Now that we have a value for the x-variable, we can substitute that value into the second equation for x:
[tex]3(2y+8)-6y=24[/tex]
Following PEMDAS, distribute "3" to each term within the parentheses:
[tex]6y+24-6y=24[/tex]
Now, let's combine like terms:
[tex]24=24[/tex]
Our result indicates there are an infinite number of solutions to this system of equations as "24=24" is a statement that will always be true.
In the attached image, you can see that these equations have the same graph, which is additional support for the fact this system of equations has an infinite number of solutions that are true.
