Question

Solve the given system of linear equations by inspection.

y = 3/5x - 5
y = -3/5x - 5
(1 point)
• (-5, 0)
O no solution
O (0, -5)
O infinitely many solutions

Answer 1

[AI-generated answer — Bot GPT 4]

O no solution

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the given system of linear equations by inspection, we need to determine if there is a single point of intersection, no solution, or infinitely many solutions.

By inspecting the equations, we can observe that the slopes are equal in magnitude but have opposite signs, indicating that the lines are parallel. Parallel lines do not intersect, which means there is no solution for this system of equations.

Therefore, the correct answer is:
O no solution.

Answer 3

[AI-generated answer — Explain Bot]

To solve the given system of linear equations by inspection, we need to find the point where the two lines intersect, if they intersect at all.

First, let's compare the two equations:

Equation 1: y = (3/5)x - 5
Equation 2: y = (-3/5)x - 5

Both equations are in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

By comparing the slopes of the two equations (3/5 and -3/5), we can see that the slopes are negative reciprocals of each other. This means that the lines are perpendicular to each other and will intersect at some point.

Next, let's set the two equations equal to each other:

(3/5)x - 5 = (-3/5)x - 5

By simplifying the equation, we get:

(3/5)x + (3/5)x = 0

(6/5)x = 0

x = 0

Now, substitute the value of x back into either equation (let's use Equation 1) to find the value of y:

y = (3/5)(0) - 5

y = -5

Therefore, the solution to the system of linear equations is (0, -5).

So, the correct answer is: O (0, -5)