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identify the two systems of equations that are equivalent a 3x 2y 12 x 3y 6 b 5x 2 2y 2 x y 6 c 5x 4y 4 4x 4y 24 d 9x 6y 3

Question

Identify the two systems of equations that are equivalent. A.- 3X +2Y=12 X – 3Y=6 B.- 5X/2 – 2Y =2 X-Y=6 C.- 5X – 4Y = 4 4X – 4Y = 24 D.- 9X + 6Y =36 2X – 2Y =12

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Answer to a math question Identify the two systems of equations that are equivalent. A.- 3X +2Y=12 X – 3Y=6 B.- 5X/2 – 2Y =2 X-Y=6 C.- 5X – 4Y = 4 4X – 4Y = 24 D.- 9X + 6Y =36 2X – 2Y =12

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1. Simplify equations in systems A and D to see if they are equivalent transformations of one another.
2. For system A:

3X + 2Y = 12

X - 3Y = 6

3. For system D, divide the first equation by 3 and the second equation by 2:

\frac{9X + 6Y}{3} = \frac{36}{3} \implies 3X + 2Y = 12

\frac{2X - 2Y}{2} = \frac{12}{2} \implies X - Y = 6

4. Subtract the equation in system D:

(X - Y) \neq (X - 3Y),

but necessary

2X - 2Y = 12

[Solution]

A \text{ and } D

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