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0.5(8w+2v)=3

8w=2-v+4w
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer:
(A)
v=1 and
w=(1)/(4)
(B)
v=4 and
w=-(1)/(4)
(c) There are infinite solutions to the system.
(D) There are no solutions to the system.

$0.5(8 w+2 v)=3$ $\newline$ $8 w=2-v+4 w$ $\newline$ Which of the following accurately describes all solutions to the system of equations shown? $\newline$ Choose $1$ answer: $\newline$ (A) $v=1$ and $w=\frac{1}{4}$ $\newline$ (B) $v=4$ and $w=-\frac{1}{4}$ $\newline$ (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.

0.5(8 w+2 v)=3

\newline

8 w=2-v+4 w

\newline

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

\newline

Choose

1

answer:

\newline

(A)

v=1

and

w=\frac{1}{4}

\newline

(B)

v=4

and

w=-\frac{1}{4}

\newline

(C) There are infinite solutions to the system.

\newline

(D) There are no solutions to the system.

Simplify Equation $1$ : Simplify the first equation. $\newline$ Given the equation $0.5(8w+2v)=3$ , distribute the $0.5$ to both terms inside the parentheses. $\newline$ $0.5 \times 8w + 0.5 \times 2v = 3$ $\newline$ $4w + v = 3$
Simplify Equation $2$ : Simplify the second equation. $\newline$ Given the equation $8w = 2 - v + 4w$ , subtract $4w$ from both sides to isolate the terms with $w$ on one side. $\newline$ $8w - 4w = 2 - v$ $\newline$ $4w = 2 - v$
Compare Simplified Equations: Compare the two simplified equations. $\newline$ We have $4w + v = 3$ from Step $1$ and $4w = 2 - v$ from Step $2$ . Notice that both equations have $4w$ as a term. We can set them equal to each other to find the relationship between $v$ and $w$ . $\newline$ $4w + v = 4w - v + 2$
Solve for v: Solve for v. $\newline$ Subtract $4w$ from both sides of the equation. $\newline$ $v = -v + 2$ $\newline$ Add $v$ to both sides to get all $v$ terms on one side. $\newline$ $2v = 2$ $\newline$ Divide both sides by $2$ to solve for v. $\newline$ $v = 1$
Substitute and Solve for $w$ : Substitute $v = 1$ into one of the simplified equations to solve for $w$ . Using the equation from Step $1$ : $4w + v = 3$ , substitute $v = 1$ . $4w + 1 = 3$ Subtract $1$ from both sides. $4w = 2$ Divide both sides by $4$ . $w = 0.5$

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