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Consider the system of equations.

y = –2x + 4,

3y + x = –3

Which statement is true of this system of equations?
Both equations are in slope-intercept form.
The first equation converted to slope-intercept form is y + 2x = 4.
The second equation converted to slope-intercept form is .y = negative one-third x minus 1
Neither equation is in slope-intercept form.

1 answer

Let's analyze each statement related to the given system of equations:

  1. Both equations are in slope-intercept form.

    • The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
    • The first equation is \(y = -2x + 4\), which is already in slope-intercept form.
    • The second equation is \(3y + x = -3\). This is not in slope-intercept form yet.

  2. The first equation converted to slope-intercept form is \(y + 2x = 4\).

    • This statement is incorrect because \(y = -2x + 4\) is the slope-intercept form. The statement \(y + 2x = 4\) is just a rearranged version of the first equation but not in slope-intercept form.

  3. The second equation converted to slope-intercept form is \(y = -\frac{1}{3}x - 1\).

    • Let's convert the second equation \(3y + x = -3\) to slope-intercept form:
      • First, isolate \(y\): \[ 3y = -x - 3 \] \[ y = -\frac{1}{3}x - 1 \]
    • This statement is indeed correct.

  4. Neither equation is in slope-intercept form.

    • This statement is false because the first equation is already in slope-intercept form.

Based on this analysis, the true statement about the system of equations is: The second equation converted to slope-intercept form is \(y = -\frac{1}{3}x - 1\).