Answer
The system has no solution since there is no point of intersection.
Work Step by Step
Graph the equations by getting the intercepts and setting arbitrary values for $x$:
Equation 1: $y = -3x$
If $x=0$
$$y = -3x$$ $$y = -3(0)$$ $$y=0$$
Hence, we have point (0,0).
If $x=1$
$$y = -3x$$ $$y = -3(1)$$ $$y=-3$$
Hence, we have point (1,-3).
If $x=-1$
$$y = -3x$$ $$y = -3(-1)$$ $$y=3$$
Hence, we have point (-1,3).
Equation 2: $3x + y = 6$
If $x=0$
$$3x + y = 6$$ $$3(0)+ y = 6$$ $$y=6$$
Hence, we have point (0,6).
if $y=0$
$$3x + y = 6$$ $$3x+ 0 = 6$$ $$3x = 6$$ $$x=2$$
Hence, we have point (2,0).
Graphing these points will give us graphs of two parallel lines. Since there is no point of intersection, therefore the system has no solution.
