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Which statement about the ordered pairs (−9, 3) and (2, −4) is true for the equation 6x−y/2=14 

A)Both ordered pair are solutions

B)Neither ordered pair are solutions

C(2,-4) is a solution to the equation
D(-9, 3) Is a solution to the problem.

Verified Answer :

linktra

C is the answer you would want to use because (2, -4) is a solution to the equation.

carlosego

Keywords:

equation, variables, ordered pairs, solution

For this case, an equation with two variables, "x" and "y" respectively, given by: \(6x- \frac {y} {2} = 14\). We must say which of the given statements is true, having as data the following ordered pairs : \((x_ {1}, y_ {1}) = (- 9, 3)\ and\ (x_ {2}, y_ {2}) = (2, -4)\) To know if the ordered pairs are equation solution , we must replace the values of x and y in the equation and observe if equality is met, if it is met, then the chosen pair is the solution of the equation.

So:

We substitute \((x_ {1}, y_ {1}) = (- 9, 3)\)

\(6 (-9) - \frac {3} {2} = 14\\-54-1.5 = 14\\-55.5 = 14\)

It is observed that the equality is not met, so \((x_ {1}, y_ {1}) = (- 9, 3)\) is not a solution of the given equation.

We substitute \((x_ {2}, y_ {2}) = (2, -4)\)

\(6 (2) - \frac {-4} {2} = 14\)

We take into account that \(- * - = +\)

\(12 + 2 = 14\\14 = 14\)

It is observed that the equality is fulfilled, thus, \((x_{2}, y_{2}) = (2, -4)\) is a solution of the given equation.

Answer:

Option C

(2, -4) is a solution to the equation