Question

How do you complete each ordered pair $\left( {2,?} \right)$ so that it is a solution to $6x - y = 7?$

Answer 1

Hint: In this question, we are going to find the missing ordered pair for the solution $6x - y = 7$
We solve this question by using a substitution method.
First we are going to substitute the value of $x$ in the given equation and then solve for $y.$
We can get the required result.

Complete step-by-step solution:
In this question, we are going to find the missing ordered pair to the given equation.
To complete the ordered pair,
First we are going to substitute $x = 2$ in the given equation and ten solve the equation for $y.$
$ \Rightarrow 6x - y = 7$
Then we get,
$ \Rightarrow 6\left( 2 \right) - y = 7$
Let us multiply the term and we get
$ \Rightarrow 12 - y = 7$
Subtract $12$from both sides of the equation we get,
$ \Rightarrow 12 - 12 - y = 7 - 12$
On simplify the term and we get
$ \Rightarrow - y = - 5$
$ \Rightarrow y = 5$
Thus we get the value $y = 5$

Therefore the unknown coordinate is equal to 5.

Note: To check the required value is correct, substitute the value into the left hand side of the given equation and if it is equal to the right hand side then they are the solution.
$ \Rightarrow 6x - y = 6\left( 2 \right) - 5$
$ \Rightarrow 12 - 5$
$ \Rightarrow 7$
When we substitute the value of $y = 5$on the left hand side of the equation, we get a value and it is equal to the right hand side.
Therefore $\left( {2,5} \right)$ is a complete ordered pair for the equation $6x - y = 7$.
Hence $\left( {2,5} \right)$ is a solution to the equation $6x - y = 7$
Hence, we get the required result.
The following are the steps to follow while solving this type of question:
To figure out if an ordered pair is a solution to an equation, we should perform a test. Identify the $x$-value in the ordered pair and plug into the equation. When you simplify, if the $y$-value we get is the same as the $y$-value in the ordered pair, then the ordered pair is indeed a solution to the equation.