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

Answer 1

To determine the number of solutions to the system of equations, we can analyze the equations given:

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

First, let's see if Equation 2 can be rewritten in a simpler form. We can divide the entire second equation by 2:

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

Now we have:

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

We can see that both equations have the same left-hand side (the expression \( 2x + y \)), but different right-hand sides (6 and 4).

Since both equations represent straight lines in a two-dimensional space, and they have the same slope (because they have the same coefficients for \( x \) and \( y \)), they are parallel lines. Since parallel lines never intersect, there are no solutions to this system of equations.

Therefore, the number of solutions to this system of equations is **0**.