We have the system of equations:
[tex]\begin{gathered} 24x+8y=8 \\ 3x+y=1 \end{gathered}[/tex]
We can solve it graphically by plotting both lines and finding the point of intersection.
The first equation can be re-aranged as:
[tex]\begin{gathered} \frac{24x+8y}{8}=\frac{8}{8} \\ 3x+y=1 \\ y=-3x+1 \end{gathered}[/tex]
It has a slope m=-3 and a y-intercept b=1.
We can find two points of the line in order to graph the line by drawing one that passes through those points.
The points will be:
[tex]\begin{gathered} x=0\longrightarrow y(0)=-3\cdot0+1=1\longrightarrow(0,1) \\ x=2=y(2)=-3\cdot2+1=-6+1=-5\longrightarrow(2,-5) \end{gathered}[/tex]
The second line is the same line as the first one: the equations are linear combinations of each other.
Then, they will be graphed as the same line.
The system will have infinite solutions: any point that lies in the line is a solution to the system.
Answer: Both lines are the same (linear combination of each other). We will have infinite solutions for the system of equations.
