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Which ordered pair is a solution of the equation?\newline2x+3y=102x+3y=10\newlineChoose 11 answer:\newline(A) Only (2,2)(2,2)\newline(B) Only (1,3)(1,3)\newline(C) Both (2,2)(2,2) and (1,3)(1,3)\newline(D) Neither

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Q. Which ordered pair is a solution of the equation?\newline2x+3y=102x+3y=10\newlineChoose 11 answer:\newline(A) Only (2,2)(2,2)\newline(B) Only (1,3)(1,3)\newline(C) Both (2,2)(2,2) and (1,3)(1,3)\newline(D) Neither
  1. Substitute (2,2)(2,2) into equation: First, we will substitute the ordered pair (2,2)(2,2) into the equation 2x+3y=102x+3y=10 and check if it holds true. If we substitute x=2x=2 and y=2y=2, we get 2⋅2+3⋅2=102\cdot 2 + 3\cdot 2 = 10.
  2. Check if it holds true: After performing the calculation, we find that 4+6=104 + 6 = 10, which is true. Therefore, the ordered pair (2,2)(2,2) is a solution to the equation.
  3. Substitute (1,3)(1,3) into equation: Next, we will substitute the ordered pair (1,3)(1,3) into the equation 2x+3y=102x+3y=10 and check if it holds true. If we substitute x=1x=1 and y=3y=3, we get 2⋅1+3⋅3=102\cdot 1 + 3\cdot 3 = 10.
  4. Check if it holds true: After performing the calculation, we find that 2+9=112 + 9 = 11, which is not equal to 1010. Therefore, the ordered pair (1,3)(1,3) is not a solution to the equation.
  5. Identify the solution: Since the ordered pair (2,2)(2,2) is a solution and the ordered pair (1,3)(1,3) is not, the correct answer is that only (2,2)(2,2) is a solution to the equation.

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