Solve the following system of equations graphically:
2x − y − 2 = 0 2x + y − 6 = 0, hence find the area of triangle
formed along X-axis.
Answers
EXPLANATION.
System of linear equation graphically.
⇒ 2x - y - 2 = 0. - - - - - (1).
⇒ 2x + y - 6 = 0. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 2x - y - 2 = 0. - - - - - (1).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) - y - 2 = 0.
⇒ - y - 2 = 0.
⇒ - y = 2.
⇒ y = - 2.
Their Co-ordinates = (0,-2).
Put the value of y = 0 in the equation, we get.
⇒ 2x - (0) - 2 = 0.
⇒ 2x - 2 = 0.
⇒ 2x = 2.
⇒ x = 1.
Their Co-ordinates = (1,0).
From equation (2), we get.
⇒ 2x + y - 6 = 0. - - - - - (2).
Put the value of x = 0 in the equation, we get.
⇒ 2(0) + y - 6 = 0.
⇒ y - 6 = 0.
⇒ y = 6.
Their Co-ordinates = (0,6).
Put the value of y = 0 in the equation, we get.
⇒ 2x + (0) - 6 = 0.
⇒ 2x - 6 = 0.
⇒ 2x = 6.
⇒ x = 3.
Their Co-ordinates = (3,0).
Both curves intersect at a point = (2,2).
As we know that,
Formula of :
Area of triangle = 1/2 x Base x Height.
⇒ Base = 3 - 1 = 2.
⇒ Height = 2.
Area of triangle = 1/2 x 2 x 2 = 2 sq. units.
Given :-
2x - y - 2 = 0
2x + y - 6 = 0
To Find :-
Area
Solution :-
In 1
2x - y - 2 = 0
2x - y = 0 + 2
2x - y = 2
Putting x = 0
2(0) - y = 2
0 - y = 2
-y = 2
y = -2
Coordinates = (0,-2)
Putting y = 0
2x - 0 = 2
2x = 2
x = 2/2
x = 1
Coordinate = (1,0)
In 2
2x + y - 6 = 0
2x + y = 0 + 6
2x + y = 6
Putting x = 0
2(0) + y = 6
0 + y = 6
y = 6
Coordinate = (0,6)
Putting y = 0
2x + 0 = 6
2x = 6
x = 6/2
x = 3
Coordinates = (3,0)
Area = 1/2 × b × h
Area = 1/2 × (3 - 1) × 2
Area = 1/2 × 2 × 2
Area = 2 units²