part a – solving by graphing\n1. solve the system by graphing:\n$y = 2x + 1$\n$y = -x + 4$

Explanation:

Step1: Find intersection algebraically

Set $2x + 1 = -x + 4$

Step2: Solve for x

$2x + x = 4 - 1$ $3x = 3$ $x = 1$

Step3: Solve for y

Substitute $x=1$ into $y=2x+1$: $y = 2(1) + 1 = 3$

Step4: Verify graph logic

The lines $y=2x+1$ (slope 2, y-int 1) and $y=-x+4$ (slope -1, y-int 4) intersect at $(1,3)$.

Answer:

The solution to the system is $(1, 3)$ (the point where the two lines intersect on a graph).