Question

How many solutions does this system have? 2x + y = 3 6x%C2%A0= 9 - 3y (1 point) Responses one one none none infinite infinite two

Answer 1

The system of equations is:

2x + y = 3
6x = 9 - 3y

To find the number of solutions, we can check if the two equations are the same or if they represent parallel lines.

First, we can rewrite the second equation as:

6x + 3y = 9

Now, we can compare the coefficients of x and y in both equations:

For x: the first equation has a coefficient of 2, while the second equation has a coefficient of 6. These coefficients are not the same.

For y: the first equation has a coefficient of 1, while the second equation has a coefficient of 3. These coefficients are not the same.

Since the coefficients of x and y are different in the two equations, the lines represented by the equations are not parallel.

Therefore, the system of equations has a unique solution, which means the correct response is "one".