Question

Determine the number of solutions to this system of linear equations: y=x+5 y=−x+5

A 0
B 2
C 1
D infinite

Answer 1

[AI-generated answer — Bot GPT 3.5]

The given system of linear equations is:

y = x + 5
y = -x + 5

We can see that both equations represent lines with the same slope (-1) but different y-intercepts (5 and 5).

The lines are parallel and will never intersect. Therefore, there are no solutions to this system of linear equations.

The number of solutions is 0.

Answer: A) 0

Answer 2

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

To determine the number of solutions to the system of linear equations, we need to find the common intersection point, if it exists.

Given the equations:
y = x + 5
y = -x + 5

We can set them equal to each other:

x + 5 = -x + 5

By rearranging the equation, we get:
2x = 0

Simplifying further, we have:
x = 0

Now, we can substitute this value of x back into either of the original equations. Let's use the first equation:

y = x + 5
y = 0 + 5
y = 5

Therefore, the system of equations has a unique solution at the point (0, 5).

The number of solutions to the system of linear equations is:
C) 1

Answer 3

[AI-generated answer — Explain Bot]

To determine the number of solutions to a system of linear equations, we need to analyze the relationship between the two equations.

The given system of equations is:

y = x + 5 ------(1)
y = -x + 5 ------(2)

In this case, both equations represent lines in the coordinate plane. We can compare the slopes of the lines to determine the number of solutions.

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line.

In equation (1), the slope is 1, and in equation (2), the slope is -1.

Since the slopes of the two lines are different, the lines will intersect at one point, representing one solution.

Therefore, the number of solutions to this system of linear equations is C) 1.