Question

Which of the following terms best describe the system of equations shown in the graph?

A consistent

B consistent and dependent

C consistent and independent

D inconsistent

Short answer

The term that describes the system of equations shown in the graph is option D ‘inconsistent’.

Step-by-step solution

Step 1. State the concept of Linear System with two variables.

A linear system of two equations with two variables is any system that can be written in the form.

$\begin{array}{l}ax+by=p\\ cx+dy=q\end{array}$

where any of the constants can be zero with the exception that each equation must have at least one variable in it.

Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.

Step 2. Explain the meaning of the terms used in the options.

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions.

Consistent:If a system has at least one solution, it is said to beconsistent.

Consistent and dependent:If aconsistentsystem has an infinite number of solutions, it isdependent. When you graph the equations, both equations represent the same line.

Consistent and independent: If aconsistentsystem has exactly one solution, it isindependent. The graphs of the lines intersect at one point.

Inconsistent: If a system has no solution, it is said to be inconsistent. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Step 3. Observe the graph and state the conclusion.

Observe the graph given below.

From the graph see that both lines are parallel and hence they won’t intersect.

Therefore, the given system of equations has no solution.

Hence, the system of equations shown in the graph are inconsistent.

Hence, option D is correct.