Question

ExpandFor each system of linear equations shown below, classify the system as "consistent dependent," "consistent Independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solutionSystem ASystem BSystem

Answer 1

System A: Consistent independent - Unique Solution: (-3,3)

System B: Inconsistent - No solution

System C: Consistent dependent - Infinite solutions

Explanation:

Let's evaluate each system:

System A:

The system A has a unique solution, since lines intersect at 1 point. For this reason, the system is consistent indepent.

We can find the solution for this system since the values for x and y are the same at insection point:

`\begin{gathered} Line1\colon y_1_{}\text{=-}(1)/(2)x+(3)/(2) \\ Line2\colon y_2\text{ =-x} \\ If\text{ }y_1\text{=}y_2 \\ Then \\ \text{-}(1)/(2)x+(3)/(2)=-x \\ -(1)/(2)x+x=-(3)/(2) \\ (-x+2x)/(2)=-(3)/(2) \\ (x)/(2)=-(3)/(2) \\ x=-(3)/(2)\cdot2 \\ x=-(6)/(2) \\ x=-3 \\ \\ Since\text{ y=-x} \\ \text{If x=-3 } \\ \text{Then y=-(-3)} \\ y=3 \end{gathered}`

Solution: (-3,3).

System B:

In this system, we have two parallel lines (same slope). So, the lines will never intersept each other.

For this reason, this system is incosistent and has no soluton.

System C:

The lines 1 and 2 are the same line.

For this reason, the system is consistent dependent and have infinite solutions.