Which of the following points are on the graphs of both the equation y=x+2 and the equation y=x²

Solution:

Given y=x+2 ….(1)

y = x² ….(2)

Solving the linear equations, (1) and (2)

x + 2 = x²

x² -x -2 = 0

(x -2)(x + 1) = 0

⇒ (x -2) = 0 ⇒ x = 2

⇒ (x +1) = 0 ⇒ x = -1

Substituting the value of x in equation(1),

y = 4 and y = 1

∴ one set of points (2, 4) and (-1, 1)

Substituting the value of x in equation(2),

y = 4 and y = 1

∴ next set of points are also (2, 4) and (-1, 1)

Graphically solving the linear equations, we get the following graph.

Thus the required points are (2, 4) and (-1, 1)

Which of the following points are on the graphs of both the equation y=x+2 and the equation y=x²

Summary:

The points on the graphs of both the equation y=x+2 and the equation y=x² are (2, 4) and (-1, 1).