Question

The graphs represent this system:   y=3x−2 −3x+y=7   How many solutions does this system have: 0, 1, or  ∞ ?(1 point)

Answer 1

To determine how many solutions the system of equations has, we can rewrite the second equation in a more standard form and analyze the two equations:

1. The first equation is already in slope-intercept form:

\[
y = 3x - 2
\]

2. The second equation can be rearranged. Starting with:

\[
-3x + y = 7
\]

We can add \(3x\) to both sides to get:

\[
y = 3x + 7
\]

Now we have the two equations:

1. \(y = 3x - 2\)
2. \(y = 3x + 7\)

Next, we observe the slopes of both equations. Both equations have a slope of 3. Since they have the same slope but different y-intercepts (-2 and +7), this means the lines are parallel.

Since parallel lines never intersect, this system of equations has **no solutions**.

Therefore, the answer is **0** solutions.