Question

Solve this system of equations by graphing. First graph the equations, and then type the solution.y=1/3x+6y=1/6x+5

Answer 1

To draw a line on the plane, we need two points on it.

Calculating two points of the equation y=x/3+6

`\begin{gathered} x=0 \\ \Rightarrow y=0+6=6 \\ \to(0,6) \\ \text{and} \\ x=3 \\ \Rightarrow y=(3)/(3)+6=7 \\ \to(3,7) \end{gathered}`

Two points of the equation y=x/6+5

`\begin{gathered} x=0 \\ \Rightarrow y=0+5=5 \\ \to(0,5) \\ x=6 \\ \Rightarrow y=(6)/(6)+5=6 \\ \to(6,6) \end{gathered}`

Then, the equation of the line y=x/3+6

And the equation of y=x/6+5 is

To solve the equation, graph both equations at the same time and look for the intersection point, as shown below

The solution is (x,y)=(-6,4)