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Determine the number of

solutions to this system of linear
equations:
2x+y=6
4x+2y=8
(1 point)
0
infinite
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 second equation. Notice that it can be simplified by dividing each term by 2:

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

This simplifies to:

\[ 2x + y = 4 \]

Now we can rewrite our system of equations as:

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

We can observe that the left-hand sides of both equations are identical (\(2x + y\)), but the right-hand sides are different (6 and 4). This means that the two equations represent parallel lines.

Since parallel lines do not intersect, there are no solutions to this system of equations.

Therefore, the correct answer is:

0