Question

Classify the system as independent, dependent, or inconsistent.y=2x-1y=-2x+5

Answer 1

To classify the equations, we will need to define some terms:

Inconsistent equations: Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables.

inconsistent equations of linear equations are equations that have no solutions in common.

An example of a set of inconsistent equations is x+2=4 and x+2=6.

Independent equation: The equations 3x + 2y = 6 and 3x + 2y = 12 are independent because any constant times one of them fails to produce the other one.

Dependent system: Equations in a dependent system can be derived from one another; they describe the same line

We can now proceed to classify the equations.

`\begin{gathered} y=2x-1 \\ \text{and} \\ y=-2x+5 \end{gathered}`

Equating the two equations

`2x-1=-2x+5`

simplifying further

`\begin{gathered} 2x+2x=1+5 \\ 4x=6 \end{gathered}`

`\begin{gathered} x=(6)/(4)=(3)/(2) \\ x=(3)/(2) \end{gathered}`

Since it has a solution (x=3/2), and also if we multiply each equation by a constant, we will have an uncommon equation.

Thus, we can classify the system as Independent