Question

How many solutions does the system of equations have?y=−2x+124y+x−20=0(1 point)ResponsesNo solutionNo solutionOne solutionOne solutionTwo solutionsTwo solutionsInfinitely many solutionsInfinitely many solutions

Answer 1

To determine how many solutions the system of equations has, we can analyze the given equations:

1. The first equation is \( y = -2x + 124 \).
2. The second equation is \( 124y + x - 20 = 0 \).

We can rewrite the second equation to express it in a more recognizable form.

Starting with:
\[ 124y + x - 20 = 0 \]

We isolate \( y \):
\[ 124y = -x + 20 \]
\[ y = -\frac{1}{124}x + \frac{20}{124} \]
\[ y = -\frac{1}{124}x + \frac{5}{31} \]

Now we have two equations:
1. \( y = -2x + 124 \)
2. \( y = -\frac{1}{124}x + \frac{5}{31} \)

Next, we can compare the slopes of these two equations:
- The slope of the first equation \( y = -2x + 124 \) is \(-2\).
- The slope of the second equation \( y = -\frac{1}{124}x + \frac{5}{31} \) is \(-\frac{1}{124}\).

Since the slopes are different, the lines represented by these equations will intersect at a single point.

**Conclusion**: The system of equations has **one solution**.