Question

If $(6,k)$ is a solution of the equation \[3x + y - 22 = 0\] , then the value of $k$ is ?

Answer 1

Hint: A pair of elements $a,b$ having the property that $(a,b) = (x,y)$ if and only if $x = a$ and $y = b$. $(a,b)$ is called the ordered pair . If the ordered pair is a solution of the given equation then the ordered pair satisfies the equation . We put the value of the variables and find the required value.

Complete step by step answer:
The given equation is $3x + y - 22 = 0$
Given the ordered pair $(6,k)$ and this ordered pair satisfy the equation
We put this ordered pair i.e., $x = 6,y = k$ respectively , we have
$3 \times 6 + k - 22 = 0$
Now solve the above equation and get the required solution
$18 + k - 22 = 0$
Taking the constant term one side and arrange these according to sign
$k - 22 + 18 = 0$
If we have $ - a + b$ ,where $a > b$ then we write $ - (a - b)$ , use this in the above equation we get
$k - (22 - 18) = 0$
Calculate i.e., subtract this and we get
$ \Rightarrow k - 4 = 0$
Adding $4$ both sides of the above equation , we get
$ \Rightarrow k = 4$
Therefore, the value of $k=4$.

Note:
When we calculate the value after putting the ordered pair in the equation , in this time take care about positive and negative signs. In this $( + )( - ) = ( - )$ and $( - )( - ) = ( + )$. If you make a mistake then you get the wrong answer . In any question if we see the ordered pair satisfy the equation then we put this in the equation and get the required answer.