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

Question

2x+y=6
4x+2y=8

(1 point)
Responses

0

infinite

2

1

Answer 1

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

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

First, let's simplify the second equation. Notice that we can divide the entire equation by 2:

\[ 2x + y = 4 \]

Now, we have the following system of equations:

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

Next, we can compare these two equations. Both have the same left-hand side (\(2x + y\)), but their right-hand sides are different (6 and 4). This indicates that there is a contradiction; the same expression cannot equal two different values simultaneously.

Thus, the two equations represent parallel lines which do not intersect.

Therefore, the system has 0 solutions.

So the answer is 0.