Answer:
The system has no solution
Step-by-step explanation:
we have
[tex]x+2y=6[/tex]
Isolate the variable y
[tex]2y=-x+6[/tex]
Divide by 2 both sides
[tex]y=-\frac{x}{2}+3[/tex] ---> equation A
[tex]y=-\frac{x}{2}+4[/tex] ---> equation B
Compare the equations
Equation A and equation B have the same slope and different y-intercept
Remember that
If two lines have the same slope, then the lines are parallel
The solution of the system is the intersection point both graphs
In this problem, the lines don't intersect, therefore, the system has no solution
using a graphing tool
The graph in the attached figure
