13.
Solve the following pair of linear equations graphically:
x + 3y = 6; 2x - 3y = 12
Also find the area of the triangle formed by the lines
representing the given equations with y-axis.
Answers
x=6
y=0
Step-by-step explanation:
x+3y=6
2x-3y=12
3x=18
x=18/3
x=6
x+3y=6
6+3y=6
3y=6-6
3y=0
y=0
EXPLANATION.
Solve the pair of linear equation graphically,
(a) = x + 3y = 6.
(b) = 2x - 3y = 12.
From equation (a) = x + 3y = 6.
put x = 0 we get,
⇒ 0 + 3y = 6.
⇒ y = 2.
Their Co-ordinate = (0,2).
put x = 3 we get,
⇒ 3 + 3y = 6.
⇒ 3y = 6 - 3.
⇒ 3y = 3.
⇒ y = 1.
Their Co-ordinate = (3,1).
put x = 6 we get,
⇒ 6 + 3y = 6.
⇒ 3y = 0.
⇒ y = 0.
Their Co-ordinate = (6,0).
From equation (b) = 2x - 3y = 12.
put x = 0 we get,
⇒ 2(0) - 3y = 12.
⇒ -3y = 12.
⇒ y = -4.
Their Co-ordinate = (0,-4).
put x = 3 we get,
⇒ 2(3) - 3y = 12.
⇒ 6 - 3y = 12.
⇒ -3y = 12 - 6.
⇒ -3y = 6.
⇒ y = -2.
Their Co-ordinate = (3,-2).
put x = 6 we get,
⇒ 2(6) - 3y = 12.
⇒ 12 - 3y = 12.
⇒ -3y = 12 - 12.
⇒ -3y = 0.
⇒ y = 0.
Their Co-ordinate = (6,0).
Red lines indicate the graph = 2x - 3y = 12.
Blue lines indicate the graph = x + 3y = 6.
Area of triangle formed by the lines representing the given equation with y-axis.
Area of triangle = 1/2 X B X H.
Area(ΔDAC) = 1/2 X 6 X 6.
Area(ΔDAC) = 18 sq. units.
