Question

Solve the given system of linear equations by inspection.

y=/35x−5


y=−3/5x−5


(1 point)
Responses

(0,−5)
left parenthesis 0 comma negative 5 right parenthesis


no solution

infinitely many solutions

(−5,0)

Answer 1

To solve the system of linear equations by inspection, we need to analyze both equations:

1. \( y = \frac{35}{1}x - 5 \) can be interpreted as:
\[ y = 35x - 5 \]

2. \( y = -\frac{3}{5}x - 5 \)

Now we can look for possible intersection points. A straightforward method is to compare the y-intercepts and slopes to see if they can yield a solution.

We can start by substituting the y-coordinate from one equation into the other. However, since this is a simple inspection, let’s check if any of the provided points satisfy both equations.

### Checking given points:

1. **Point (0, -5)**:
- Substitute \( x = 0 \) into the first equation:
\[ y = 35(0) - 5 = -5 \] (satisfies the first equation)
- Substitute \( x = 0 \) into the second equation:
\[ y = -\frac{3}{5}(0) - 5 = -5 \] (satisfies the second equation)
- Therefore, \( (0, -5) \) is a solution.

2. **Point (-5, 0)**:
- Substitute \( x = -5 \) into the first equation:
\[ y = 35(-5) - 5 = -175 - 5 = -180 \] (does not satisfy the first equation)

3. **No solution**:
- Not applicable, as we found a common solution.

4. **Infinitely many solutions**:
- Not applicable, as the lines are not the same.

From the analysis, the solution to the system of equations is:

\((0, -5)\)