# 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?

Jul 14, 2016

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 $\textcolor{g r e e n}{x}$ for the equation $\textcolor{g r e e n}{4 x - y = 13}$ (looking for integer values of $\textcolor{g r e e n}{y}$ 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 $\textcolor{red}{4 x + 5 y = - 17}$
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))