Question

The graph solves this system of equations. What is the solution to the system? Use the drop-down menus to explain your answer.

4x + 6y = 8
y = −23
x + 13


Two parallel lines that both have negative slopes.

The system of equations has
Choose...
because the two lines are
Choose...
.

Answer 1

To solve the system of equations given, we can analyze the provided equations:

1. The first equation is \(4x + 6y = 8\).
2. The second equation is \(y = -23\).

We can simplify the first equation to determine its slope. We can rewrite it in slope-intercept form (\(y = mx + b\)):

1. Rearranging \(4x + 6y = 8\):
\[
6y = -4x + 8
\]
\[
y = -\frac{2}{3}x + \frac{4}{3}
\]

Now we have two equations:
1. \(y = -\frac{2}{3}x + \frac{4}{3}\) (with a slope of \(-\frac{2}{3}\))
2. \(y = -23\) (which is a horizontal line at \(y = -23\))

### Analysis of the lines:
- The first equation is a line with a negative slope.
- The second equation is a horizontal line.
- Therefore, the two lines cannot be parallel as one has a negative slope and the other is horizontal.

### Conclusion:
Since one line is horizontal and the other has a negative slope, the system of equations has **no solutions** because the two lines are **not parallel**. They would intersect at some point if they were not parallel lines (which they aren't, considering their slopes).

Therefore, filling in the drop-down menus, we can say:
- The system of equations has **no solutions** because the two lines are **not parallel**.