Determine the number of solutions to this system of linear equations: y=x+5 y=−x+5 (1 point) 0 1 infinite 2

Answer 1

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

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

We can set the two equations equal to each other since they both equal \( y \):

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

Next, we solve for \( x \):

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

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

Using the first equation:

\[ y = 0 + 5 = 5 \]

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

Since there is one unique solution where the lines intersect, the number of solutions to the system of linear equations is:

\[ \boxed{1} \]