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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

infinite
infinite

2
2

1

1 answer

To determine the number of solutions to the system of equations:

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

We can analyze the equations.

First, let's simplify the second equation:

\[ 4x + 2y = 8 \]

Dividing the entire equation by 2 gives:

\[ 2x + y = 4 \]

Now we compare the two equations:

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

The left-hand sides of both equations are identical, but the right-hand sides are different (6 and 4). This indicates that the two equations represent parallel lines that never intersect.

Since there are no points (x, y) that satisfy both equations simultaneously, the system has:

0 solutions.

So, the answer is:

0