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

Question

y=x+5

y=−x+5
(1 point)
Responses

0
0

1
1

infinite
infinite

2

Answer 1

To determine the number of solutions to the system of linear equations given by:

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

we can analyze the equations:

1. The first equation, \( y = x + 5 \), represents a line with a slope of 1.
2. The second equation, \( y = -x + 5 \), represents a line with a slope of -1.

Next, we can find the intersection point of the two lines (if they intersect). To do this, we can set the two equations equal to each other:

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

Now, let's solve for \( x \):

\[ 2x + 5 = 5 \] \[ 2x = 0 \] \[ x = 0 \]

Now, we can substitute \( x = 0 \) back into either equation to find \( y \):

Using the first equation:

\[ y = 0 + 5 = 5 \]

Thus, the intersection point is \( (0, 5) \).

Since the two lines have different slopes, they will intersect at exactly one point. Therefore, the system of equations has exactly one solution.

The answer is:

1