Question

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.

Answer 1

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

Answer 2

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