Question

system b
line 1: $y = -x + 3$
line 2: $y = x + 1$
graph of two lines intersecting
this system of equations is:
\bigcirc inconsistent
\bigcirc consistent dependent
\bigcirc consistent independent
this means the system has:
\bigcirc a unique solution
\quad solution: $(\square, \square)$
\bigcirc no solution
\bigcirc infinitely many solutions

Explanation:

Step1: Analyze system type

A consistent independent system has two distinct lines (different slopes) intersecting at one point. Line 1: \( y = -x + 3 \) (slope -1), Line 2: \( y = x + 1 \) (slope 1). Different slopes, so they intersect (one solution). So system is consistent independent.

Step2: Find solution

Set \( -x + 3 = x + 1 \). Solve: \( -x - x = 1 - 3 \) → \( -2x = -2 \) → \( x = 1 \). Substitute \( x = 1 \) into \( y = x + 1 \): \( y = 2 \). So solution is (1,2).

Answer:

This system of equations is: consistent independent
This means the system has: a unique solution
Solution: \( (1, 2) \)