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4y−3x=404y-3x=40\newline4y=3x−304y=3x-30\newlineWhich of the following accurately describes all solutions to the system of equations shown?\newlineChoose 11 answer:\newline(A) x=0x=0 and y=0y=0\newline(B) x=53x=\frac{5}{3} and y=454y=\frac{45}{4}\newline(C) There are infinite solutions to the system.\newline(D) There are no solutions to the system.

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Q. 4y−3x=404y-3x=40\newline4y=3x−304y=3x-30\newlineWhich of the following accurately describes all solutions to the system of equations shown?\newlineChoose 11 answer:\newline(A) x=0x=0 and y=0y=0\newline(B) x=53x=\frac{5}{3} and y=454y=\frac{45}{4}\newline(C) There are infinite solutions to the system.\newline(D) There are no solutions to the system.
  1. Analyze Equations: Analyze the given system of equations.\newlineWe are given two equations:\newline11) 4y−3x=404y - 3x = 40\newline22) 4y=3x−304y = 3x - 30\newlineLet's compare the two equations to see if they are equivalent or different.
  2. Simplify Second Equation: Simplify the second equation to match the form of the first equation.\newlineThe second equation can be rewritten by adding 3x3x to both sides:\newline4y=3x−304y = 3x - 30\newline4y+30=3x4y + 30 = 3x\newlineNow, subtract 3030 from both sides to get it in the form of the first equation:\newline4y=3x−304y = 3x - 30
  3. Identify Contradiction: Notice the contradiction.\newlineThe first equation states that 4y−3x=404y - 3x = 40, while the second equation, after simplification, states that 4y−3x=−304y - 3x = -30. These two statements cannot be true at the same time for the same values of xx and yy. This means there is a contradiction, and the system of equations does not have a solution where both equations are satisfied simultaneously.
  4. Conclude No Solutions: Conclude the number of solutions. Since the two equations are contradictory and cannot be satisfied by the same pair of (x,y)(x, y), there are no solutions to the system of equations.

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