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.

Bytelearn · Accepted Answer

Simplify Equation: Simplify the first equation. Given: 0.5(8w+2v)=3 Multiply both sides by 2 to eliminate the fraction: 8w + 2v = 6Isolate Variable: Isolate the variable w in the second equation. Given: 8w = 2 - v + 4w Subtract 4w from both sides to get: 4w = 2 - vSolve for w: Solve for w in terms of v. Divide both sides by 4: w = (2 - v)/4Substitute in First Equation: Substitute w from Step 3 into the first equation. Replace w in 8w + 2v = 6 with (2 - v)/4: 8((2 - v)/4) + 2v = 6Simplify Substitution: Simplify the equation. Distribute 8 into (2 - v)/4: 2(2 - v) + 2v = 6Expand and Combine: Expand and combine like terms. 4 - 2v + 2v = 6Check Validity: Check if the equation is valid. Since 4 - 2v + 2v simplifies to 4, we have 4 = 6, which is not true.Determine Solutions: Determine the nature of the solutions. Since we arrived at a false statement, this implies that there are no values of v and w that can satisfy both equations simultaneously. Therefore, there are no solutions to the system.

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