Answer:
(-7,-17) is the right solution.
They distributed wrong. Instead of -2(3x+4) equaling -6x+8, it should have been -6x-8.
Explanation:
Let's solve it along with them.
We have the system:
y=3x+4
3x-2y=13
They solved it by substitution. They replaced the 2nd y with what the first y equaled which was (3x+4):
3x-2(3x+4)=13
To solve this you would first need to distribute the -2 to the terms inside the ( ):
3x-6x-8=13 (This is the line that is different from theirs; this is where they went incorrect.)
-3x-8=13
Add 8 on both sides:
-3x=21
Divide both sides by -3:
x=21/-3
Simplify:
x=-7
If y=3x+4 and x=-7, then y=3(-7)+4=-21+4=-17.
So the solution is (-7,-17).
Let's check it:
y=3x+4 for (x,y)=(-7,-17)?
-17=3(-7)+4
-17=-21+4
-17=-17
Since this equation is true then (-7,-17) is on y=3x+4.
3x-2y=13 for (x,y)=(-7,-17)?
3(-7)-2(-17)=13
-21+34=13
13=13
Since this equation is true then (-7,-17) is on 3x-2y=13.
Therefore it is a common point between the lines and is the solution (or intersection).