Question

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

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2x + y = 6

4x+2y=8 (1 point)

COURSE TOOLS

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O infinite

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Answer 1

To determine the number of solutions for the given system of equations:

1. **First Equation:**
\[
2x + y = 6
\]

2. **Second Equation:**
\[
4x + 2y = 8
\]

We can manipulate the second equation for comparison. Notice that the second equation can be simplified by dividing through by 2:

\[
\frac{4x}{2} + \frac{2y}{2} = \frac{8}{2}
\]
This simplifies to:

\[
2x + y = 4
\]

Now we have the following system of equations:

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

These two equations represent two lines in a two-dimensional plane. However, they have different constant terms (6 and 4) but the same coefficients for \(x\) and \(y\).

Since both equations represent lines that are parallel (they have the same slope and y-intercept), they will never intersect. Hence, there are no points \((x, y)\) that satisfy both equations simultaneously.

Thus, the system of equations has **no solution**.

**Answer:** 0 solutions.