Question

How many solutions does the following system have?

Answer 1

Answer:

Option D. No solutions

Step-by-step explanation:

we have

$3x+2y=1$ -----> equation A

$-9x-6y=3$ ----> equation B

Multiply by -3 both sides equation A

$-3(3x+2y)=-3(1)$

$-9x-6y=-3$ -----> 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

$-9(0)-6y=-3$ ----->$y=0.5$

The y-intercept is the point (0,0.5)

Equation B

$-9(0)-6y=3$ ----->$y=-0.5$

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