Question

If $\left( 4,19 \right)$ is a solution of the equation $y=ax+3$, then a is equal to
A. 3
B. 4
C. 5
D. 6

Answer 1

Hint: To find the value of a we will substitute the values $x=4$ and $y=19$ in the given equation as $\left( 4,19 \right)$ is the solution of the given equation so it must satisfied the equation. Then simplifying the obtained equation we will get the desired answer.

Complete step-by-step answer:
We have been given an equation $y=ax+3$ and a solution of the equation $\left( 4,19 \right)$.
We have to find the value of a.
Now, as given that $\left( 4,19 \right)$ is the solution of the equation $y=ax+3$, so the values must satisfy the given equation. So let us substitute the values $x=4$ and $y=19$ in the given equation. Then we will get
$\begin{align}
  & \Rightarrow y=ax+3 \\
 & \Rightarrow 19=a\times 4+3 \\
\end{align}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 19=4a+3 \\
 & \Rightarrow 19-3=4a \\
 & \Rightarrow 16=4a \\
 & \Rightarrow \dfrac{16}{4}=a \\
 & \Rightarrow 4=a \\
 & \Rightarrow a=4 \\
\end{align}$
Hence we get the value of a as 4.

So, the correct answer is “Option B”.

Note: Be careful while substituting the values of x and y in the equation. Always remember that the point is of the form $\left( x,y \right)$, so substitute values accordingly. We can also verify the obtained answer by substituting the value in the given equation. By substituting the value of a in the given equation we will get
$\begin{align}
  & \Rightarrow y=ax+3 \\
 & \Rightarrow 19=4\times 4+3 \\
\end{align}$
Now, simplifying the above obtained equation we will get
\[\begin{align}
  & \Rightarrow 19=16+3 \\
 & \Rightarrow 19=19 \\
\end{align}\]
Hence we get LHS=RHS
So the obtained solution is correct.