Question

Solve the system by graphing. 24x + 8y =83x y = 1

Answer 1

We have the system of equations:

`\begin{gathered} 24x+8y=8 \\ 3x+y=1 \end{gathered}`

We can solve it graphically by plotting both lines and finding the point of intersection.

The first equation can be re-aranged as:

`\begin{gathered} (24x+8y)/(8)=(8)/(8) \\ 3x+y=1 \\ y=-3x+1 \end{gathered}`

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:

`\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}`

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.