Question

How do you find the value of $y$ that makes $\left( {3,y} \right)$ a solution to the equation $3x - y = 4$?

Answer 1

Hint: To find the value of $y$ for which $\left( {3,y} \right)$ is a solution of the equation $3x - y = 4$, we will substitute $\left( {3,y} \right)$ in the equation $3x - y = 4$, then by operating accordingly the equation, we can find the value of $y$ for which the point $\left( {3,y} \right)$ satisfies the equation $3x - y = 4$. Hence, it will be our required answer. So, let us see how to solve the problem.

Complete step by step answer:
Given to us in the question, $\left( {3,y} \right)$ is a solution to $3x - y = 4$.
So, we can substitute $x = 3$ in the equation.
So, by substituting the value, we get,
$\left( {3.3} \right) - y = 4$
$ \Rightarrow 9 - y = 4$
Now, by subtracting $9$ from both sides of the equation, we get
$ \Rightarrow - y = 4 - 9$
$ \Rightarrow - y = - 5$
Now, by multiplying both sides of the equation with $ - 1$, we get
$y = 5$
Therefore, the value of $y$ for which $\left( {3,y} \right)$ is a solution to $3x - y = 4$ is $5$.

Note: We can also solve this question by using graphs. First we will plot the equation on the graph, then by finding the point $\left( {3,y} \right)$ on the graph, we can find what is the value of $y$. Now, in order to do so, we have to find the point $x = 3$, which will be a line parallel to the y-axis passing through $x = 3$. The point where the line will intersect the graph of the equation $3x - y = 4$ will be the value of $y$ for which the point $\left( {3,y} \right)$ is a solution of the equation $3x - y = 4$. Using graphs to find the solution of an equation is called the geometrical approach of solving equations. And, the above method is called the algebraic approach of solving equations.