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

y = 3+5
y = -x + 5 (1 point)

1 answer

First, let's simplify the first equation:

  1. \( y = 3 + 5 \) \[ y = 8 \]

Now, we have the following two equations:

  1. \( y = 8 \)
  2. \( y = -x + 5 \)

Next, we can substitute the value of \( y \) from the first equation into the second equation to find \( x \):

\[ 8 = -x + 5 \]

Now, solve for \( x \):

  1. Add \( x \) to both sides: \[ 8 + x = 5 \]

  2. Subtract 5 from both sides: \[ x = 5 - 8 \] \[ x = -3 \]

Now we have a specific solution:

  • \( x = -3 \)
  • \( y = 8 \)

Thus, the system of equations has a unique solution at the point \((-3, 8)\).

Therefore, the number of solutions to the system of linear equations is 1.