Question

Solve the following system of equations and state whether the system is dependent, independent, or inconsistent.4x+3y=12And4x-3y=12

Answer 1

Given:

`\begin{gathered} 4x+3y=12 \\ 4x-3y=12 \end{gathered}`

Required:

To solve the system of equation using graph and to state whether the system is dependent, independent, or inconsistent.

Step-by-step explanation:

Consider the equation

`4x+3y=12`

When x=0,

`\begin{gathered} 0+3y=12 \\ 3y=12 \\ y=(12)/(3) \\ y=4 \end{gathered}`

When x=3,

`\begin{gathered} 12+3y=12 \\ 3y=12-12 \\ 3y=0 \\ y=0 \end{gathered}`

Now consider the equation

`4x-3y=12`

When x=0,

`\begin{gathered} 0-3y=12 \\ -3y=12 \\ y=-(12)/(3) \\ y=-4 \end{gathered}`

When x= 3,

`\begin{gathered} 12-3y=12 \\ -3y=12-12 \\ -3y=0 \\ y=0 \end{gathered}`

The graph of the given system of equation is,

The blue graph is graph of 4x+3y=12 and the black graph is graph of

4x-3y=12.

The two line crosses at the point (3,0).

Therefore the solution is

`\begin{gathered} x=3 \\ y=0 \end{gathered}`

Here the solution is one.

Therefore the consistent system has exactly one solution, it is independent .

Final Answer:

The solution of the given system of equation is

`\begin{gathered} x=3 \\ y=0 \end{gathered}`

The consistent system has exactly one solution, it is independent .