Answer:
one solution, no solution, infinitely many solutions
Step-by-step explanation:
I rearranged the first equation into x=6-2y
plug that into the second equation
2(6-2y)-3y=26
12-4y-3y=26
12-7y=26
-7y=14
y=-2
Then you plug that into one of the equations
x+2(-2)=6
x-4=6
x=10
The solution to the first system is (10,-2)
the second system already has one equation as something equal to a single variable so you just plug that into the other one
4x-2(2x-4)=-6
4x -4x +8 =-6
8=-6
this is a false statement so the system of equation has no solution
Lastly I rearranged the first equation into y=2x-4 and then plug that in
6x-3(2x-4)=12
6x-6x+12=12
12=12
this statement is true so the system of equations has infinite solutions
