{:[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.

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

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Precalculus

Solve rational equations

Full solution

s-2=9

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3 r-4 s=16

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

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Choose

1

answer:

\newline

(A)

r=8

and

s=2

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(B)

r=20

and

s=11

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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 = $20$