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$7p = 9(p + q) + 11$ $\newline$ $99 + 3 = 4(7q +p)$ $\newline$ Consider the system of equations. If $p, 9$ is the solution to the system, then what is the value of $-p - 9$ ?

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Write and solve direct variation equations

Full solution

Q.

7p = 9(p + q) + 11

\newline

99 + 3 = 4(7q +p)

\newline

Consider the system of equations. If

p, 9

is the solution to the system, then what is the value of

-p - 9

?

Simplify first equation: Step $1$ : Simplify the first equation. $\newline$ Original equation: $7p = 9(p + q) + 11$ $\newline$ Distribute the $9$ : $7p = 9p + 9q + 11$ $\newline$ Subtract $9p$ from both sides: $-2p = 9q + 11$
Simplify second equation: Step $2$ : Simplify the second equation. $\newline$ Original equation: $99 + 3 = 4(7q + p)$ $\newline$ Simplify left side: $102 = 4(7q + p)$ $\newline$ Divide both sides by $4$ : $25.5 = 7q + p$

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