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{:[t-5=(1)/(3)(u+15)-5],[t=(2)/(3)(u+9)]:}
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer:
(A)
u=-18 and
t=-6
(B)
u=-3 and
t=4
(C) There are infinite solutions to the system.
(D) There are no solutions to the system.
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$\begin{aligned} t-5 & =\frac{1}{3}(u+15)-5 \\ t & =\frac{2}{3}(u+9) \end{aligned}$ $\newline$ Which of the following accurately describes all solutions to the system of equations shown? $\newline$ Choose $1$ answer: $\newline$ (A) $u=-18$ and $t=-6$ $\newline$ (B) $u=-3$ and $t=4$ $\newline$ (C) There are infinite solutions to the system. $\newline$ (D) There are no solutions to the system. $\newline$ Show calculator

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Compare linear and exponential growth

Full solution

Q.

\begin{aligned} t-5 & =\frac{1}{3}(u+15)-5 \\ t & =\frac{2}{3}(u+9) \end{aligned}

\newline

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

\newline

Choose

1

answer:

\newline

(A)

u=-18

and

t=-6

\newline

(B)

u=-3

and

t=4

\newline

(C) There are infinite solutions to the system.

\newline

(D) There are no solutions to the system.

\newline

Show calculator

Write Equations: Write down the equations. $\newline$ Equation $1$ : $t - 5 = \frac{1}{3}(u + 15) - 5$ $\newline$ Equation $2$ : $t = \frac{2}{3}(u + 9)$
Simplify Equation $1$ : $\newline$ Step $2$ : Simplify Equation $1$ . $\newline$ $t - 5 = \frac{1}{3}(u + 15) - 5$ $\newline$ $t - 5 = \frac{1}{3}u + 5 - 5$ $\newline$ $t - 5 = \frac{1}{3}u$ $\newline$ Add $5$ to both sides: $\newline$ $t = \frac{1}{3}u + 5$
Simplify Equation $2$ : $\newline$ Step $3$ : Simplify Equation $2$ . $\newline$ $t = \frac{2}{3}(u + 9)$ $\newline$ $t = \frac{2}{3}u + 6$
Set Equations Equal: $\newline$ Step $4$ : Set the simplified equations equal to each other. $\newline$ $\frac{1}{3}u + 5 = \frac{2}{3}u + 6$
Solve for u: $\newline$ Step $5$ : Solve for $u$ . $\newline$ Subtract $\frac{1}{3}u$ from both sides: $\newline$ $5 = \frac{1}{3}u + 6$ $\newline$ Subtract $6$ from both sides: $\newline$ $-1 = \frac{1}{3}u$ $\newline$ Multiply both sides by $3$ : $\newline$ $u = -3$
Substitute u and Find t: $\newline$ Step $6$ : Substitute $u = -3$ back into one of the original equations to find $t$ . $\newline$ Using $t = \frac{2}{3}(u + 9)$ : $\newline$ $t = \frac{2}{3}(-3 + 9)$ $\newline$ $t = \frac{2}{3}(6)$ $\newline$ $t = 4$
Verify Solution: $\newline$ Step $7$ : Verify the solution by substituting $u = -3$ and $t = 4$ into the other equation. $\newline$ Using $t - 5 = \frac{1}{3}(u + 15) - 5$ : $\newline$ $4 - 5 = \frac{1}{3}(-3 + 15) - 5$ $\newline$ $-1 = \frac{1}{3}(12) - 5$ $\newline$ $-1 = 4 - 5$ $\newline$ $-1 = -1$ (True)

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

Simplify any fractions.

\newline

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\newline

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\newline

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\newline

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