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Which ordered pair is a solution of the equation?

-3x+5y=2x+3y
Choose 1 answer:
(A) Only 
(2,4)
(B) Only 
(3,3)
(C) Both 
(2,4) and 
(3,3)
(D) Neither

Which ordered pair is a solution of the equation?\newline3x+5y=2x+3y-3x+5y=2x+3y\newlineChoose 11 answer:\newline(A) Only (2,4)(2,4)\newline(B) Only (3,3)(3,3)\newline(C) Both (2,4)(2,4) and (3,3)(3,3)\newline(D) Neither

Full solution

Q. Which ordered pair is a solution of the equation?\newline3x+5y=2x+3y-3x+5y=2x+3y\newlineChoose 11 answer:\newline(A) Only (2,4)(2,4)\newline(B) Only (3,3)(3,3)\newline(C) Both (2,4)(2,4) and (3,3)(3,3)\newline(D) Neither
  1. Combine Like Terms: First, we need to simplify the equation by combining like terms. We can do this by moving all terms involving xx to one side of the equation and all terms involving yy to the other side.3x+5y=2x+3y-3x + 5y = 2x + 3y
  2. Move xx and yy Terms: Subtract 2x2x from both sides to get all the xx terms on one side.\newline3x2x+5y=3y-3x - 2x + 5y = 3y
  3. Subtract 2x2x: Combine the xx terms.\newline5x+5y=3y-5x + 5y = 3y
  4. Combine xx Terms: Now, subtract 3y3y from both sides to get all the yy terms on one side.\newline5x+5y3y=0-5x + 5y - 3y = 0
  5. Subtract 3y3y: Combine the yy terms.\newline5x+2y=0-5x + 2y = 0
  6. Combine yy Terms: Now we have a simplified equation: 5x+2y=0-5x + 2y = 0. We can check each ordered pair to see if it satisfies this equation.
  7. Simplified Equation: Let's check the ordered pair (2,4)(2,4).\newlineSubstitute x=2x = 2 and y=4y = 4 into the equation.\newline5(2)+2(4)=0-5(2) + 2(4) = 0\newline10+8=0-10 + 8 = 0\newline20-2 \neq 0\newlineThis ordered pair does not satisfy the equation.
  8. Check (2,4): (2,4): Now let's check the ordered pair (3,3) (3,3) . Substitute x=3 x = 3 and y=3 y = 3 into the equation. 5(3)+2(3)=0 -5(3) + 2(3) = 0 15+6=0 -15 + 6 = 0 90 -9 \neq 0 This ordered pair also does not satisfy the equation.
  9. Check (3,3) (3,3) : Since neither (2,4) (2,4) nor (3,3) (3,3) satisfy the equation 5x+2y=0 -5x + 2y = 0 , the correct answer is (D) Neither.

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