If each of ( – 2, 2), (0, 0) and (2, – 2) is a solution of a linear equation in x and y, then the equation is

Question

Philoid · Accepted Answer

We will find the solution by trying all the options.

Let the equation be x – y = 0

For the point ( – 2, 2),

x = – 2 and y = 2

then, x – y = – 2 – 2 = – 4

For the point (0, 0),

x = 0 and y = 0

then, x – y = 0 – 0 = 0

For the point (2, – 2),

x = 2 and y = – 2

then, x – y = 2 – ( – 2) = 2 + 2 = 4

Since, all the solutions are different therefore, the given points ( – 2, 2), (0, 0) and (2, – 2) does not satisfy x – y

Let the equation be x + y = 0

For the point ( – 2, 2),

x = – 2 and y = 2

then, x + y = – 2 + 2 = 0

For the point (0, 0),

x = 0 and y = 0

then, x + y = 0 + 0 = 0

For the point (2, – 2),

x = 2 and y = – 2

then, x + y = 2 + ( – 2) = 2 – 2 = 0

Since, all the solutions are same therefore, the given points ( – 2, 2), (0, 0) and

(2, – 2) satisfies x + y. Hence, the equation is x + y