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. The first equation is s - 2 = 9. To solve for s, add 2 to both sides of the equation. s - 2 + 2 = 9 + 2 s = 11Substitute s in second equation: Substitute the value of s into the second equation. The second equation is 3r - 4s = 16. Substitute s = 11 into this equation. 3r - 4(11) = 16 3r - 44 = 16Solve for r: Solve the second equation for r. Add 44 to both sides of the equation to isolate the term with r. 3r - 44 + 44 = 16 + 44 3r = 60 Now, divide both sides by 3 to solve for r. 3r / 3 = 60 / 3 r = 20Check solution: Check the solution with both equations. First, check the solution in the first equation s - 2 = 9. 11 - 2 = 9 9 = 9 This is true. Now, check the solution in the second equation 3r - 4s = 16. 3(20) - 4(11) = 16 60 - 44 = 16 16 = 16 This is also true.

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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 trigonometric equations

Full solution

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

\newline

(D) There are no solutions to the system.

Solve for s: Solve the first equation for s. $\newline$ The first equation is $s - 2 = 9$ . To solve for s, add $2$ to both sides of the equation. $\newline$ $s - 2 + 2 = 9 + 2$ $\newline$ $s = 11$
Substitute $s$ in second equation: Substitute the value of $s$ into the second equation. $\newline$ The second equation is $3r - 4s = 16$ . Substitute $s = 11$ into this equation. $\newline$ $3r - 4(11) = 16$ $\newline$ $3r - 44 = 16$
Solve for r: Solve the second equation for r. $\newline$ Add $44$ to both sides of the equation to isolate the term with $r$ . $\newline$ $3r - 44 + 44 = 16 + 44$ $\newline$ $3r = 60$ $\newline$ Now, divide both sides by $3$ to solve for $r$ . $\newline$ $\frac{3r}{3} = \frac{60}{3}$ $\newline$ $r = 20$
Check solution: Check the solution with both equations. $\newline$ First, check the solution in the first equation $s - 2 = 9$ . $\newline$ $11 - 2 = 9$ $\newline$ $9 = 9$ $\newline$ This is true. $\newline$ Now, check the solution in the second equation $3r - 4s = 16$ . $\newline$ $3(20) - 4(11) = 16$ $\newline$ $60 - 44 = 16$ $\newline$ $16 = 16$ $\newline$ This is also true.