Question

Which shows the graphical point of intersection for the representation below?

Answer 1

Consider the given system of equations,

`\begin{gathered} x-y=3 \\ 7x-y=-3 \end{gathered}`

One possible way to identify the correct graph is to obtain the solution of the above system of equations. And then look for the graph that correctly represents the point of intersection.

Subtract the first equation from the second equation,

`\begin{gathered} (7x-y)-(x-y)=-3-3 \\ 7x-y-x+y=-6 \\ 7x-x+0=-6 \\ 6x=-6 \\ x=(-6)/(6) \\ x=-1 \end{gathered}`

Substitute this value in the first equation and obtain the corresponding 'y' value,

`\begin{gathered} -1-y=3 \\ -y=3+1 \\ -y=4 \\ y=-4 \end{gathered}`

So the common and unique solution to the system of equations is (-1 -4).

In the graphical method, this point must be the point of intersection of the lines.

Now, observe the given three graphs carefully.

Clearly, it is the 3rd graph whi