Answer:
The system has one solution
Both lines have the same y-intercept
The solution is the intersection of the 2 lines
Step-by-step explanation:
we have
[tex]2y=x+10[/tex]
isolate the variable y
[tex]y=\frac{x}{2}+5[/tex] ----> equation A
[tex]3y=3x+15[/tex]
isolate the variable y
[tex]y=x+5[/tex] ----> equation B
we have two lines with different slopes and equal y-intercepts
so
The solution is the intersection point both graphs
The intersection point is the y-intercept
so
The solution is the point (0,5)
Verify each statement
1) The system has one solution
The statement is true
The solution is the point (0,5)
2) The system graphs parallel lines
The statement is false
The lines are not parallel, because the slopes are different
3) Both lines have the same slope
The statement is false
The slopes are different. the slope of line A is m=1\2 and the slope of line B is m=1
4) Both lines have the same y-intercept
The statement is true
The y-intercept b=5
5) The equations graph the same line
The statement is false
Because the lines are different
6) The solution is the intersection of the 2 lines
The statement is true
