Question

How many solutions does the following system have?

3x+2y=1
-9x-6y=3
A. Infinitely many solutions
B. Two solutions
C. One solution
D. No solutions

Answer 1

Option D. No solutions

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