Question

Without graphing, classify each system

independent, dependent, or inconsistent.

3y + 2x= 12
36 - 9y = -6x

Answer 1

The solution to the system of equations be:

`y=4,\:x=0`

As the consistent system of equations has only one solution, it is independent.

Explanation:

Given the system of equations

`3y + 2x= 12`

`36 - 9y = -6x`

solving the system of equations

`\begin{bmatrix}3y+2x=12\\ 36-9y=-6x\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}3y+2x=12\\ -9y+6x=-36\end{bmatrix}`

`\mathrm{Multiply\:}3y+2x=12\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:9y+6x=36`

`\begin{bmatrix}9y+6x=36\\ -9y+6x=-36\end{bmatrix}`

so

`-9y+6x=-36`

`+`

`\underline{9y+6x=36}`

`12x=0`

`\begin{bmatrix}9y+6x=36\\ 12x=0\end{bmatrix}`

solve 12x=0 for x

`12x=0`

Divide both sides by 12

`(12x)/(12)=(0)/(12)`

`x=0`

`\mathrm{For\:}9y+6x=36\mathrm{\:plug\:in\:}x=0`

`9y+6\cdot \:0=36`

`9y=36`

Divide both sides by 9

`(9y)/(9)=(36)/(9)`

`y=4`

Thus, the solution to the system of equations be:

`y=4,\:x=0`

As the consistent system of equations has only one solution, it is independent.