Question

Systems of Linear Equations Unit Test
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Question
Determine the number of solutions to this system of linear equations:
2x+y=6

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

0
0

2
2

1
1

infinite

Answer 1

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

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

We can first rearrange the first equation to express \(y\) in terms of \(x\):
\[y = 6 - 2x\]

Next, we'll simplify the second equation:
\[4x + 2y = 8\]
Dividing the entire equation by 2 gives us:
\[2x + y = 4\]

Now, we have the following two equations:
1. \(2x + y = 6\)
2. \(2x + y = 4\)

Now we compare both equations:
- The left-hand sides are identical, but the right-hand sides (6 and 4) are different.

This indicates that the two lines represented by these equations are parallel and do not intersect.

Therefore, the system of equations has **no solutions**.

The answer is **0**.