Chapter 3 Linear Systems and Matrices - 3.1 Solve Linear Systems by Graphing - 3.1 Exercises - Skill Practice - Page 157: 32

The solution is $(2.5,1.5)$

Given: $y = |x -1|$ $y=-x+4$ When $x \leq 1$ the first equation will be $y=-x+1$. The graph has slope $m=-1$, so that part of the first equation is parallel with $y=-x+4$. For the right part, the graphs intersect at $(2.5,1.5)$. Check again: $y = |x -1|$ $1.5= |2.5 -1|$ $1.5=1.5$ $1.5=-2.5+4$ $1.5=1.5$ The solution is $(2.5,1.5)$.