Question

How do you complete $ 3x - 2y = 6 $ , and the ordered pairs are $ \left( {0,..} \right) $ , $ \left( {2,..} \right) $ and $ \left( {..,3} \right) $ ?

Answer 1

Hint: In this question, we need to calculate the unknown element in ordered pairs $ \left( {0,..} \right) $ , $ \left( {2,..} \right) $ and $ \left( {..,3} \right) $ . For determining the value, we will substitute the value of the known element in the given equation $ 3x - 2y = 6 $ . And equating the equation to the unknown value and by solving it, we will determine the required.

Complete step by step solution:
The ordered pairs given are $ \left( {0,..} \right) $ , $ \left( {2,..} \right) $ and $ \left( {..,3} \right) $ .
The equation given is $ 3x - 2y = 6 $ .
In order to calculate the unknown element in an ordered pair, we need to substitute the value of the known element in the given equation.
Let us consider the ordered pair $ \left( {0,..} \right) $ .
Here the value of $ x $ is given and we need to determine the value of $ y $ .
Now, let us substitute the value of $ x $ in the given equation $ 3x - 2y = 6 $ and solve it for $ y $ .
Thus, we have,
 $ 3\left( 0 \right) - 2y = 6 $
 $ - 2y = 6 $
 $ y = - \dfrac{6}{2} $
Therefore, $ y = - 3 $
Hence, the pair is $ \left( {0, - 3} \right) $ .
Next, let us consider the ordered pair $ \left( {2,..} \right) $ .
Here the value of $ x $ is given and we need to determine the value of $ y $ .
Now, let us substitute the value of $ x $ in the given equation $ 3x - 2y = 6 $ and solve it for $ y $ .
Thus, we have,
 $ 3\left( 2 \right) - 2y = 6 $
 $ 6 - 2y = 6 $
 $ - 2y = 6 - 6 $
 $ - 2y = 0 $
Therefore, $ y = 0 $
Hence, the pair is $ \left( {2,0} \right) $ .
Next, let us consider the ordered pair $ \left( {..,3} \right) $ .
Here the value of $ y $ is given and we need to determine the value of $ x $ .
Now, let us substitute the value of $ y $ in the given equation $ 3x - 2y = 6 $ and solve it for $ x $ .
Thus, we have,
 $ 3x - 2\left( 3 \right) = 6 $
 $ 3x - 6 = 6 $
 $ 3x = 6 + 6 $
 $ x = \dfrac{{12}}{3} $
Therefore, $ x = 4 $
Hence, the pair is $ \left( {4,3} \right) $ .

Note: It is important to note here that ordered pair usually refers to a set of two numbers used to locate a point in a coordinate plane. When an ordered pair refers to the location of a point in the coordinate plane, they are called the coordinates of the point.