{:[3x+2y=4(x-y-6)],[6(y+x)=7x-24]:} Which of the following accurately describes all solutions to the system of equations shown? Choose 1 answer: (A) x=3 and y=-1 (B) x=12 and y=-2 (c) There are infinite solutions to the system. (D) There are no solutions to the system.

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{:[3x+2y=4(x-y-6)],[6(y+x)=7x-24]:} Which of the following accurately describes all solutions to the system of equations shown? Choose 1 answer: (A)  x=3 and  y=-1 (B)  x=12 and  y=-2 (c) There are infinite solutions to the system. (D) There are no solutions to the system.

Bytelearn · Accepted Answer

Expand and simplify the first equation: Expand the first equation to simplify it. 3x + 2y = 4(x - y - 6) 3x + 2y = 4x - 4y - 24 Now, move all terms involving variables to one side and constants to the other side. 2y + 4y = 4x - 3x - 24 6y = x - 24Rearrange terms in the first equation: Simplify the second equation. 6(y + x) = 7x - 24 6y + 6x = 7x - 24 Now, move all terms involving variables to one side and constants to the other side. 6y = 7x - 6x - 24 6y = x - 24Simplify the second equation: Compare the two simplified equations. From Step 1: 6y = x - 24 From Step 2: 6y = x - 24 We can see that both equations are identical, which means every solution to one equation is also a solution to the other.Rearrange terms in the second equation: Determine the type of solution set. Since both equations are identical, there are infinitely many solutions to the system. Any value of x and y that satisfies one equation will satisfy the other.

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