Answer
The system has one 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.
---
The 1st equation is in slope-intercept form.
Rewrite the 2nd equation, solving for y:
$ 4x-y=-3\qquad$ ... add $y+3$ to both sides
$4x+3=y$
$ y=4x+3\qquad$ ... slope-intercept form.
$\left[\begin{array}{llll}
& \text{slope, }m & , & \text{y-intercept , } b\\
\text{first line: } & -1/4 & & 3\\
\text{second line: } & 4 & & 3
\end{array}\right]$
The two lines have different slopes $\Rightarrow$ they have ONE intersection point.
The system has one solution.
