How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 3y − x = 4 and y + 2x = −1?

Feb 29, 2016

Answer:

Graph each of the linear equations using a pair of points for each.
If the graphed lines intersect then the equations are consistent (and have a mutual solution at their intersection point).

Explanation:

For the equation $\textcolor{red}{3 y - x = 4}$
I found (arbitrary) solutions:
color(white)("XXX")color(red){:(color(white)("X")x,color(white)("X")y),(-4,color(white)("X")0),(color(white)("X")2,color(white)("X")2) :}

For the equation $\textcolor{b l u e}{y + 2 x = 1}$
I found (again, arbitrary) solutions:
color(white)("XXX")color(blue){:(color(white)("X")x,color(white)("X")y),(color(white)("X")0,color(white)("X")1),(color(white)("X")2,-3) :}

Using each pair of points, we can plot lines:

or, combining them on a single graph:

We can see that the equations are consistent (since they intersect).