Question

Solve the following of equations and state whether the system is dependent, independent, or inconsistent by graphing1/2x+3/4y=12x-3y=4

Answer 1

Given:

`\begin{gathered} (1)/(2)x+(3)/(4)y=1 \\ \\ 2x-3y=4 \end{gathered}`

Find-:

The system is dependent, independent, or inconsistent

Explanation-:

`\begin{gathered} (1)/(2)x+(3)/(4)y=1 \\ \\ (2x)/(4)+(3y)/(4)=1 \\ \\ (2x+3y)/(4)=1 \\ \\ 2x+3y=4................(1) \end{gathered}`
`2x-3y=4............(2)`

Add both equations then,

`\begin{gathered} 2x+3y+2x-3y=4+4 \\ \\ 4x=8 \\ \\ x=(8)/(4) \\ \\ x=2 \end{gathered}`

So value of y is:

`\begin{gathered} 2x-3y=4 \\ \\ 2(2)-3y=4 \\ \\ 4-3y=4 \\ \\ 3y=4-4 \\ \\ y=(0)/(3) \\ \\ y=0 \end{gathered}`

Value of y is 0

The solution for this system of equation is the point (2,0) and this set of equation is consistent since it has one solution at exactly one point. Thus this is consistent and independent.