Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `4x - y = 13` and `4x + 5y = -17`?

Answer 1

Find two coordinates for each equation that satisfy the equation;
plot the points; draw a line through the two points for each equation; the point of intersection will be the common solution.

Explanation:

Testing various values of `color(green)(x)` for the equation `color(green)(4x-y=13)` (looking for integer values of `color(green)(y)` since these are easier to plot,
I came up with

#color(green)({: (underline(x),color(white)("XXX"),underline(y)), (0,,-13), (5,,7) :})#

Similarly for `color(red)(4x+5y=-17)`
I found as possible solutions:

#color(red)({: (underline(x),color(white)("XXX"),underline(y)), (-3,,-1), (7,,-9) :})#

Plotting each of these pairs of solutions and drawing a line through the pair of points for each gives:

Since the lines intersect, the equations are consistent
with an apparent solution at `color(blue)(""(2,-5))`