Question

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.

Answer 1

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 \(y = -\frac{1}{3}x - 1\).**