Question

I need to know the system of equations graphed below

Answer 1

As given by the question

There are given that the graph of a system of equation.

Now,

Solve every system of the equation which is given in options for the intersect value i.e. (1, 3).

And,

Then, the value of x = 1 and y = 3, will be the correct option because according to the graph, the intersection point is (1, 3).

Now,

we can directly solve option B for the intersection value.

So,

From the system of the equation of option B;

`\begin{gathered} y-3x=0\ldots(1) \\ x-y=-2\ldots(2) \end{gathered}`

Now,

From the equation (1):

`\begin{gathered} y-3x=0 \\ y=3x\ldots(3) \end{gathered}`

Put the value of y into the equation (2):

`\begin{gathered} x-y=-2 \\ x-3x=-2 \\ -2x=-2 \\ x=1 \end{gathered}`

Then,

Put the value of x into equation (3) to find the value of y.

So,

`\begin{gathered} y=3x \\ y=3(1) \\ y=3 \end{gathered}`

The value of x is 1 and the value of y is 3, which means the intersect value is (1, 3).

Hence, the correct option is B.