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Determine the number of solutions to this system of linear equations:

2x+y=6

4x+2y=8
(1 point)
Responses

0
0

2
2

infinite
infinite

1

1 answer

To determine the number of solutions for the given system of linear equations, we can analyze the equations:

  1. \( 2x + y = 6 \)
  2. \( 4x + 2y = 8 \)

We can notice that the second equation can be simplified. Divide the entire equation by 2:

\[ \frac{4x + 2y}{2} = \frac{8}{2} \]

This simplifies to:

\[ 2x + y = 4 \]

Now we have the simplified system:

  1. \( 2x + y = 6 \)
  2. \( 2x + y = 4 \)

Next, we can see that these two equations represent parallel lines because they have the same slope (the coefficient of \( x \) is the same in both equations), but different y-intercepts (6 and 4).

Since parallel lines do not intersect, this system has no solutions.

Thus, the number of solutions to the system of equations is:

0