Solve graphically the following system of linear equations (use graph sheet) :
x − 3y = 3
2x + 3y = 6
Also, find the area of the triangle formed by these two lines and the y-axis.
Answers
The area of the triangle formed by these two lines and the y-axis = 9/2
The equation of the lines -
x − 3y = 3 -----(1)
2x + 3y = 6 -----(2)
From (1) x= 3+3y
Putting the value x in (2) -
2 (3+3y) +3y =6
=> 9y=0
=> y=0
x=3 , y=0
The two lines will intersect at A(3,0)
The triangle will be formed by the points A(3,0) , B(0,-1) and C(0,2) as in the figure
Area of the triangle = area of OAB + area of OAC
=> ( 1/2 × 3 × 1 ) + ( 1/2 × 3 ×2)
=> 3/2 + 6/2
=> 9/2
Area of the triangle formed = 9/2
Answer:
Explanation:
The area of the triangle formed by these two lines and the y-axis = 9/2
The equation of the lines -
x − 3y = 3 -----(1)
2x + 3y = 6 -----(2)
From (1) x= 3+3y
Putting the value x in (2) -
2 (3+3y) +3y =6
=> 9y=0
=> y=0
x=3 , y=0
The two lines will intersect at A(3,0)
The triangle will be formed by the points A(3,0) , B(0,-1) and C(0,2) as in the figure
Area of the triangle = area of OAB + area of OAC
=> ( 1/2 × 3 × 1 ) + ( 1/2 × 3 ×2)
=> 3/2 + 6/2
=> 9/2
Area of the triangle formed = 9/2