Answer
The system has no solution.
Work Step by Step
Observing the equation form $\quad y=mx+b$,
(slope-intercept form,)
we read slope = $m$, and the y-intercept of the line is at $(0,b)$
Two lines with different slopes intersect at ONE intersection point.
Two lines with same slopes:
- are parallel, if their y-intercepts are different, or
- coincide, if if the y-intercepts are equal as well.
---
Rewrite each equation, solving for y:
$\left[\begin{array}{lllll}
3x+y=0 & /-3x & | & y=-3x+1 & \\
y=-3x+0 & & | & &
\end{array}\right]$
$\left[\begin{array}{llll}
& \text{slope, }m & , & \text{y-intercept , } b\\
\text{first line: } & -3 & & 0\\
\text{second line: } & -3 & & 1
\end{array}\right]$
These lines have equal slopes, but their y-intercepts differ,
$\Rightarrow$ they are parallel, and have no intersections.
The system has no solution.
