Respuesta :
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:
[tex]\begin{gathered} Q+P=30-P+P, \\ Q+P=30. \end{gathered}[/tex]Subtracting Q to the above equation we get:
[tex]\begin{gathered} Q+P-Q=30-Q, \\ P=30-Q\text{.} \end{gathered}[/tex]2) Adding 5P to the second equation we get:
[tex]\begin{gathered} Q+5P=20-5P+5P, \\ Q+5P=20. \end{gathered}[/tex]Subtracting Q to the above equation we get:
[tex]\begin{gathered} Q+5P-Q=20-Q, \\ 5P=20-Q\text{.} \end{gathered}[/tex]Dividing the above equation by 5 we get:
[tex]\begin{gathered} \frac{5P}{5}=\frac{20-Q}{5}, \\ P=4-\frac{Q}{5}\text{.} \end{gathered}[/tex]3) Adding 2P to the third equation we get:
[tex]\begin{gathered} 6Q+2P=14-2P+2P, \\ 6Q+2P=14. \end{gathered}[/tex]Subtracting 6Q to the above equation we get:
[tex]\begin{gathered} 6Q+2P-6Q=14-6Q, \\ 2P=14-6Q\text{.} \end{gathered}[/tex]Dividing the above equation by 2 we get:
[tex]\begin{gathered} \frac{2P}{2}=\frac{14-6Q}{2}, \\ P=7-3Q\text{.} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 1)P=30-Q, \\ 2)P=4-\frac{Q}{5}, \\ 3)P=7-3Q\text{.} \end{gathered}[/tex]