Keywords:
equation, variables, ordered pairs, solution
For this case, an equation with two variables, "x" and "y" respectively, given by: [tex]6x- \frac {y} {2} = 14[/tex]. We must say which of the given statements is true, having as data the following ordered pairs : [tex](x_ {1}, y_ {1}) = (- 9, 3)\ and\ (x_ {2}, y_ {2}) = (2, -4)[/tex] 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 [tex](x_ {1}, y_ {1}) = (- 9, 3)[/tex]
[tex]6 (-9) - \frac {3} {2} = 14\\-54-1.5 = 14\\-55.5 = 14[/tex]
It is observed that the equality is not met, so [tex](x_ {1}, y_ {1}) = (- 9, 3)[/tex] is not a solution of the given equation.
We substitute [tex](x_ {2}, y_ {2}) = (2, -4)[/tex]
[tex]6 (2) - \frac {-4} {2} = 14[/tex]
We take into account that [tex]- * - = +[/tex]
[tex]12 + 2 = 14\\14 = 14[/tex]
It is observed that the equality is fulfilled, thus, [tex](x_{2}, y_{2}) = (2, -4)[/tex] is a solution of the given equation.
Answer:
Option C
(2, -4) is a solution to the equation
