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.

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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.

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Simplify Equation 1: Simplify the first equation. Given the equation 0.5(8w+2v)=3, distribute the 0.5 to both terms inside the parentheses. 0.5 * 8w + 0.5 * 2v = 3 4w + v = 3Simplify Equation 2: Simplify the second equation. Given the equation 8w = 2 - v + 4w, subtract 4w from both sides to isolate the terms with w on one side. 8w - 4w = 2 - v 4w = 2 - vCompare Simplified Equations: Compare the two simplified equations. 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. 4w + v = 4w - v + 2Solve for v: Solve for v. Subtract 4w from both sides of the equation. v = -v + 2 Add v to both sides to get all v terms on one side. 2v = 2 Divide both sides by 2 to solve for v. v = 1Substitute 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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