Answer
The system has infinitely many solutions.
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:
$\left[\begin{array}{llllll}
3x-y=6 & /+y-6 & | & x=\frac{y}{3} +2 & /\times 3 & \\
3x-6=y & & | & 3x=y +6 & /-6 & \\
y=3x-6 & & | & y=3x-6 & &
\end{array}\right]$
.
$\left[\begin{array}{llll}
& \text{slope, }m & , & \text{y-intercept , } b\\
\text{first line: } & 3 & & -6\\
\text{second line: } & 3 & & -6
\end{array}\right]$
These lines have equal slopes, and their y-intercepts are equal,
$\Rightarrow$ the lines coincide (the equations represent one and the same line).
The system has infinitely many solutions.
