Determine the number of solutions to this system of linear equations:

Question

y=x+5

y=−x+5
(1 point)
Responses

2

1

infinite

0

Answer 1

To determine the number of solutions to the system of equations, let's analyze the two equations:

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

To find the intersection (which represents the solution(s) to the system), we can set the right sides of the equations equal to each other:

\[ x + 5 = -x + 5 \]

Now, we can solve for \( x \):

1. Add \( x \) to both sides: \[ x + x + 5 = 5 \] \[ 2x + 5 = 5 \]

2. Subtract \( 5 \) from both sides: \[ 2x = 0 \]

3. Divide by \( 2 \): \[ x = 0 \]

Now that we have \( x \), we can substitute it back into either equation to find \( y \). Using the first equation:

\[ y = 0 + 5 = 5 \]

Thus, we have one solution to the system, which is \( (0, 5) \).

Since the two equations intersect at exactly one point, the number of solutions to the system of equations is:

1