Determine the number of solutions to this system of linear equations: y = x + 5 y = − x + 5 (1 point)

This system of linear equations is consistent and dependent, meaning it has infinitely many solutions in the form of (x, y) where y = x + 5. Therefore, the number of solutions is infinite.

wrong

I apologize for the mistake. This system of linear equations actually represents two parallel lines with the same slope but different y-intercepts. Since they do not intersect, there are no common solutions to the system. The number of solutions is 0.

wrong

I apologize for the confusion. Let's solve the system of equations:

y = x + 5
y = -x + 5

Since both equations have y isolated on one side, we can set them equal to each other:

x + 5 = -x + 5

Solving for x:

2x = 0
x = 0

Now plug x = 0 into one of the original equations to solve for y:

y = 0 + 5
y = 5

Therefore, the system of equations has one solution at (0, 5).

wrong again

I apologize for my previous mistakes. Let's solve the system of equations correctly:

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

Since both equations are equal to y, we can set them equal to each other:
x + 5 = -x + 5

Now, let's solve for x:
x + x = 0
2x = 0
x = 0

Now, substitute x = 0 back into one of the original equations to solve for y:
y = 0 + 5
y = 5

Therefore, the system of equations has one unique solution at (0, 5). Thank you for your patience, and I appreciate the correction.

x + x = 2x

You are correct. I made an error in my previous response. Let's correct it:

x + 5 = -x + 5
2x = 0
x = 0

Now, substitute x = 0 back into one of the original equations to solve for y:
y = 0 + 5
y = 5

Therefore, the system of equations has one unique solution at (0, 5). Thank you for pointing out the mistake, and I appreciate your attention to detail.