Answer:
Option D. No solutions
Step-by-step explanation:
we have
[tex]3x+2y=1[/tex] -----> equation A
[tex]-9x-6y=3[/tex] ----> equation B
Multiply by -3 both sides equation A
[tex]-3(3x+2y)=-3(1)[/tex]
[tex]-9x-6y=-3[/tex] -----> equation C
Compare equation B and equation C
Equation B and equation C are parallel lines with different y-intercept
Verify
For x=0
Equation C
[tex]-9(0)-6y=-3[/tex] ----->[tex]y=0.5[/tex]
The y-intercept is the point (0,0.5)
Equation B
[tex]-9(0)-6y=3[/tex] ----->[tex]y=-0.5[/tex]
The y-intercept is the point (0,-0.5)
therefore
Lines do not intersect
The system has no solution
see the attached figure to better understand the problem
