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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

1 answer

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.