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

1 answer

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.

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