Help with algebra 1 please 10 points.?

Question

3. y = 3x - 1 and y = 3x + 3. How many solutions exist for the system?

one solution
no solution
infinitely many solutions
cannot be determined

Answer 1

3x - 1 = 3x + 3

Subtract 3x from each side.

-1 = 3 this is false

Any value would satisfy both equations.

The problem is that the equations are of two lines that are parallel so they never touch each other...

lets think that "y" is 4 for example:

y = 3x - 1

4 = 3x - 1

Add 1 to each side. 3x = 5.

Divide each side by 3.

x= 5/3 ("x" should be 5/3 to satisfy the first equation)

y = 3x + 3

4=3x+3

Subtract 3 from each side. 3x = 1

Divide each side by 3.

x=1/3 (but "x" should be 1/3 to satisfy the second equation)

Any value satisfies both equations.

Which is infinite.

Comments

The system of equations are y = 3x - 1 and y = 3x + 3.

Since, the given two lines are parallel lines, the system has no solution.

Option B is the correct choice.