Question

Organize each of the following equations to express P as a function of QQ = 30-P Q=20-5P6Q=14-2P

Answer 1

To organize each given equation to express P as a function of Q we will solve each equation for P.

1) Adding P to the first equation we get:

`\begin{gathered} Q+P=30-P+P, \\ Q+P=30. \end{gathered}`

Subtracting Q to the above equation we get:

`\begin{gathered} Q+P-Q=30-Q, \\ P=30-Q\text{.} \end{gathered}`

2) Adding 5P to the second equation we get:

`\begin{gathered} Q+5P=20-5P+5P, \\ Q+5P=20. \end{gathered}`

Subtracting Q to the above equation we get:

`\begin{gathered} Q+5P-Q=20-Q, \\ 5P=20-Q\text{.} \end{gathered}`

Dividing the above equation by 5 we get:

`\begin{gathered} (5P)/(5)=(20-Q)/(5), \\ P=4-(Q)/(5)\text{.} \end{gathered}`

3) Adding 2P to the third equation we get:

`\begin{gathered} 6Q+2P=14-2P+2P, \\ 6Q+2P=14. \end{gathered}`

Subtracting 6Q to the above equation we get:

`\begin{gathered} 6Q+2P-6Q=14-6Q, \\ 2P=14-6Q\text{.} \end{gathered}`

Dividing the above equation by 2 we get:

`\begin{gathered} (2P)/(2)=(14-6Q)/(2), \\ P=7-3Q\text{.} \end{gathered}`

Answer:

`\begin{gathered} 1)P=30-Q, \\ 2)P=4-(Q)/(5), \\ 3)P=7-3Q\text{.} \end{gathered}`