We have been given a table of values of a function. We are asked to determine whether the given function is linear or nonlinear.
We know that a function is linear when its rate of change (slope) is constant.
Let us find slope for each of the given points using slope formula.
Similarly, we will find the slopes using other given coordinates.
Since the rate of change for each set of points is , so the rate of change is constant.
Therefore, the given function is linear.
Given:
The system of equations is:
Line A:
Line B:
To find:
The solution of given system of equations.
Solution:
We have,
...(i)
...(ii)
Equating (i) and (ii), we get
Divide both sides by 2.
Substituting in (i), we get
The solution of system of equations is (-4,-8).
Now verify the solution by substituting in the given equations.
This statement is true.
Similarly,
This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.