Question

one solution, no solution, or many solutions quick check
determine the number of solutions to this system of linear equations:
y = x + 5
y = -x + 5 (1 point)
0
1
2
infinite

Explanation:

Step1: Set equations equal

Since \( y = x + 5 \) and \( y = -x + 5 \), set \( x + 5 = -x + 5 \).

Step2: Solve for x

Add \( x \) to both sides: \( 2x + 5 = 5 \). Subtract 5: \( 2x = 0 \), so \( x = 0 \).

Step3: Find y

Substitute \( x = 0 \) into \( y = x + 5 \): \( y = 0 + 5 = 5 \). One solution.

Answer:

1 (corresponding to the option with "1")