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{:[s-2=9],[3r-4s=16]:}
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer:
(A)
r=8 and
s=2
(B)
r=20 and
s=11
(c) There are infinite solutions to the system.
(D) There are no solutions to the system.

$s-2=9$ $\newline$ $3 r-4 s=16$ $\newline$ Which of the following accurately describes all solutions to the system of equations shown? $\newline$ Choose $1$ answer: $\newline$ (A) $r=8$ and $s=2$ $\newline$ (B) $r=20$ and $s=11$ $\newline$ (C) There are infinite solutions to the system. $\newline$ D There are no solutions to the system.

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Solve rational equations

Full solution

Q.

s-2=9

\newline

3 r-4 s=16

\newline

Which of the following accurately describes all solutions to the system of equations shown?

\newline

Choose

1

answer:

\newline

(A)

r=8

and

s=2

\newline

(B)

r=20

and

s=11

\newline

(C) There are infinite solutions to the system.

\newline

D There are no solutions to the system.

Solve for s: Solve the first equation for s. $\newline$ Given the equation $s - 2 = 9$ , we can solve for s by adding $2$ to both sides of the equation. $\newline$ $s - 2 + 2 = 9 + 2$ $\newline$ $s = 11$
Substitute value of $s$ : Substitute the value of $s$ into the second equation. $\newline$ Now that we know $s = 11$ , we can substitute this value into the second equation $3r - 4s = 16$ to find the value of $r$ . $\newline$ $3r - 4(11) = 16$ $\newline$ $3r - 44 = 16$
Solve for r: Solve the second equation for r. $\newline$ To find the value of r, we add $44$ to both sides of the equation. $\newline$ $3r - 44 + 44 = 16 + 44$ $\newline$ $3r = 60$ $\newline$ Now, divide both sides by $3$ to isolate r. $\newline$ $\frac{3r}{3} = \frac{60}{3}$ $\newline$ r = $20$

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