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

Question

2x+y=6

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

infinite
infinite

1
1

0
0

2

Answer 1

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

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

First, we can simplify the second equation. Notice that the second equation can be rewritten as:

\[ 4x + 2y = 8 \implies 2(2x + y) = 8 \implies 2x + y = 4 \]

Now we have:

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

These two equations show that:

• The first equation represents a line in the plane where \(y\) is determined by \(x\) such that \(y = 6 - 2x\).
• The second equation represents another line where \(y = 4 - 2x\).

Since these lines have the same slope (both are of the form \(y = mx + b\)) but different y-intercepts (6 and 4), they are parallel and will never intersect.

Thus, there are no solutions to this system of equations.

The answer is: 0