Question

Find three different solution of the equation $2x-y=7$

Answer 1

Hint: This equation represents a line in the XY- plane. A line has an infinite number of solutions. Therefore, for this line also there are an infinite number of solutions out of which we only have to find 3 solutions. To find these solutions, we will write ‘y’ in term of ‘x’ and then we will give ‘x’ any three integral values which will give us corresponding values for ‘y’ and hence we will get our answer.

Complete step by step answer:
Now, we have been given the equation :
$2x-y=7$
We will now, from this equation, write ‘y’ in terms of ‘x’. This will give us:
$\begin{align}
  & \Rightarrow 2x-y=7 \\
 & \Rightarrow 2x=7+y \\
\end{align}$
$\Rightarrow y=2x-7$ .....(1)
 Thus ’y’ in term of ‘x’ is written as $y=2x-7$
Now, we will give ‘x’ any three integral values of our choice and note the corresponding values of ‘y’ and we will get 3 different solutions.

Let $x=0$
Putting this value of x in equation (1) we get:
$\begin{align}
  & \Rightarrow y=2\left( 0 \right)-7 \\
 & \Rightarrow y=0-7 \\
 & \Rightarrow y=-7 \\
\end{align}$
Therefore, the first solution will be (0,-7)

Let $x=1$
Putting this value of ‘x’ in equation (1) we get :
$\begin{align}
  & \Rightarrow y=2\left( 1 \right)-7 \\
 & \Rightarrow y=2-7 \\
 & \Rightarrow y=-5 \\
\end{align}$
Therefore, second solution will be (1,-5)

Let $x=2$
Putting this value of x is equation (1) we get:
$\begin{align}
  & \Rightarrow y=2\left( 2 \right)-7 \\
 & \Rightarrow y=4-7 \\
 & \Rightarrow y=-3 \\
\end{align}$
Therefore, third solution will be (2,-3)

Thus, our 3 distinct solutions are (0,-7), (1,-5) and (2,-3)

Note: We can also get our answer by writing ‘x’ in terms of ‘y’ and then assigning different integral values to ‘y’ and noting down the corresponding values of ‘x’. Also, it is not necessary to assign integral values to ‘x’ or ‘y’ in either of the two cases. We just assigned them integral values so that the calculation will be easy.