Final answer:
To graphically solve the system y = 4x - 1 and 2x + y = 5, rewrite the second equation as y = -2x + 5. Plot the lines by starting with their y-intercepts (at -1 and 5) and using slopes to find additional points. The solution occurs at the intersection, (1, 3).
Step-by-step explanation:
To solve the system of equations y = 4x - 1 and 2x + y = 5 graphically, start by expressing the second equation as y = -2x + 5.
Plot the lines on a coordinate system, beginning with their respective y-intercepts at -1 and 5.
Utilize the slopes to determine additional points for each line: for y = 4x - 1, from (0, -1), move up 4 units and right 1 unit to (1, 3); for y = -2x + 5, from (0, 5), move down 2 units and right 1 unit to (1, 3).
The lines intersect at (1, 3), revealing that x=1 and y=3 satisfy both equations.