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Which ordered pair is a solution of the equation?

\[ x+7y=17\]
Choose 1 answer:
Choose 1 answer:
(Choice A) Only
\[(10,1)\]
A
Only
\[(10,1)\]
(Choice B) Only
\[(-4,3)\]
B
Only
\[(-4,3)\]
(Choice C) Both
\[(10,1)\] and
\[(-4,3)\]
C
Both
\[(10,1)\] and
\[(-4,3)\]
(Choice D) Neither
D
Neither

1 answer

To determine which ordered pair is a solution of the equation \( x + 7y = 17 \), we will substitute each pair into the equation and see if it holds true.

  1. For the pair (10, 1): \[ x = 10, \quad y = 1 \] Substitute into the equation: \[ 10 + 7(1) = 10 + 7 = 17 \] This is true, so (10, 1) is a solution.

  2. For the pair (-4, 3): \[ x = -4, \quad y = 3 \] Substitute into the equation: \[ -4 + 7(3) = -4 + 21 = 17 \] This is also true, so (-4, 3) is also a solution.

Given that both ordered pairs satisfy the equation, the correct choice is:

(Choice C) Both \( (10, 1) \) and \( (-4, 3) \).