Question

How do you find the ordered pairs for \[3x - 2y = 6\]?

Answer 1

Hint: Here in this question we have to find the ordered pairs for the given equation. The ordered pair is a combination of x and y. So here we substitute the value of x and y as 0 and determine the values. Hence we obtain the result for the given question.

Complete step-by-step answer:
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.
Now consider the given equation \[3x - 2y = 6\]
Substitute the value of x as 0. we have
\[ \Rightarrow 3(0) - 2y = 6\]
On simplifying we have
\[ \Rightarrow - 2y = 6\]
Divide the above equation by -2
\[ \Rightarrow y = - 3\]
Therefore the value of y is -3 when the value of x is 0.
Substitute the value of y as 0. we have
\[ \Rightarrow 3x - 2(0) = 6\]
On simplifying we have
\[ \Rightarrow 3x = 6\]
Divide the above equation by 3
\[ \Rightarrow x = 2\]
Therefore the value of x is 2 when the value of y is 0.
Therefore the ordered pairs for the \[3x - 2y = 6\] is (0, -3) and (2, 0).
Just we have determined only two ordered pairs, but the equation has infinitely many ordered pairs.
So, the correct answer is “(0, -3) and (2, 0).”.

Note: The ordered pair is written in the common parenthesis. Firstly it has x value and then comma and then followed by the value of y. The values of x and y depends on the equation. Just we have substituted the value of x and y as 0 and determined the ordered pair. Hence we can substitute the value of x and y anything.