Question

Write any four solutions of the given equation $x + y = 2.$

Answer 1

Hint: In order to find the solution, we know that the given equation follows the line equation with an infinite number of solutions, so by putting the different values of y, we will get the corresponding value of x.

Complete step-by-step answer:
Given equation $x + y = 2.$
For any solution we will put a value of y and by solving for the value of x we will get the corresponding value of x.
We know that the given equation represents a straight line.
Now by taking the value of y= 1, we get
$
  x + 1 = 2 \\
  x = 1 \\
$
$(1,1)$ is one of the solutions of the given equation.
Now, by taking the value of y = 2, we get
$
  x + 2 = 2 \\
  x = 0 \\
$
$\therefore (0,2)$ is the second solution of the given equation.
By taking y = 3, we get
$
  x + 3 = 2 \\
  x = - 1 \\
$
$\therefore ( - 1,3)$ is also the solution of the given equation.
By taking the value of y = 4, we get
\[
  x + 4 = 2 \\
  x = - 2 \\
\]
$\therefore (- 2,4)$ is another solution to the given equation.
Hence, four solutions of the given equation are $(1,1),(0,2),( - 1,3){\text{ and }}( - 2,4).$

Note: In order to solve these types of questions, where we need to find the solutions of given equation; first write down the equation and substitute the value of x or y and the corresponding value of y or x can be calculated. Also the solution of an equation always satisfies the equation. In the above question we have a straight line and it has infinite solutions. Also if the equation of parabola or circle is given we will find the solution of the equation in the same way.