Question

Write any two solutions of the equation $x + y = 7$.

Answer 1

Hint: In order to find the solution of the question try to consider some values of any of the unknown variables on your own and then use the equation to find the value of another unknown variable by substituting the value.

Complete step-by-step answer:
Given equation is $x + y = 7$
The above equation is of general form $ax + by + c = 0$ , which represents a line. As we know that the line has an infinite number of points so an infinite number of solutions exists for the equation.
For finding any particular solution, we will consider a value of y and substitute in the equation.
Let us take $y = 1$
So, after substitution, we have
$
  \because x + y = 7 \\
   \Rightarrow x + 1 = 7 \\
   \Rightarrow x = 7 - 1 \\
   \Rightarrow x = 6 \\
 $
So, $\left( {6,1} \right)$ is one of the solutions of the equation.
Now, by taking the value $y = 2$ , we get
$
  \because x + y = 7 \\
   \Rightarrow x + 2 = 7 \\
   \Rightarrow x = 7 - 2 \\
   \Rightarrow x = 5 \\
 $
So, $\left( {5,2} \right)$ is another solution of the equation.
Hence, two solutions of the given equation are $\left( {6,1} \right){\text{ and }}\left( {5,2} \right)$

Note: As mentioned earlier the equation represents a line so it will have infinitely many solutions. A student may obtain a solution other than the above one. The problem can also be solved by plotting the graph of the equation and finding the solution from the points there. We were given just one equation and told to find out two unknowns. As we know that the number of unknowns that can be found out from the “n” number of equations is “n” only. So we had to consider a value on our own.