Question

use the graph to determine the number of solutions the system has. then state whether the system of equations is consistent or inconsistent and if it is independent or dependent.
y = x - 1
y = -x + 1
a) 1 solution; consistent and independent
b) infinitely many solutions; consistent and dependent
c) 1 solution; consistent and dependent
d) no solution; inconsistent

Explanation:

1. First, analyze the two equations \(y = x - 1\) (a line with slope 1, y - intercept - 1) and \(y=-x + 1\) (a line with slope - 1, y - intercept 1).
2. To find the number of solutions, we can look at their intersection. Since the slopes of the two lines are different (\(1

eq - 1\)), the lines are not parallel and will intersect at exactly one point.

1. A system of equations with at least one solution is consistent. Since the two equations represent distinct lines (different slopes and different y - intercepts), they are independent (not the same line, so not dependent). So the system has 1 solution, is consistent, and is independent.

Answer:

A) 1 solution; consistent and independent