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

y=x+5

y=−x+5
(1 point)
Responses

1
1

infinite
infinite

0
0

2

1 answer

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

To find the point of intersection, we can set the two equations equal to each other:

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

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

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

Now that we have \( x = 0 \), we can substitute it back into either equation to find \( y \). Using the first equation:

\[ y = 0 + 5 = 5 \]

So, the point of intersection is \( (0, 5) \).

Since the two lines intersect at exactly one point, the system of equations has one solution.

Final Answer: 1