Question

the area of triangle formed by the lines 2x + 3y =12, x-y-1=0 and x=0, is


a) 7.5sq units
b)6.5units
C)6units
d)7sq.units​

Answer 1

derive x and y from equations and plot graph

Answer 2

Answer:

Given Equation 1: 2x + 3y = 12 Equation 2: x – y = 1 Equation 3: x = 0 To calculate the Area at first we solve the Equation 1 & 2 Simultaneously by method of substitution. We substitute the value of x from Equation 2 in Equation 1 to get the value of y Equation 2: x – y = 1 ⇒ x = y + 1 Equation 1: 2x + 3y = 12 Substituting the value from equation 2 we get 2(y + 1) + 3y = 12 ⇒ 2y + 2 + 3y = 12 ⇒ 5y = 10 ⇒ y = 2 Putting the value in Equation 1 we get x = 2 + 1 ⇒ x = 3 So both this lines passes through ( 3 , 2) Let this Coordinate name be P1 Equation 3 is the equation for y axis Equation 1 meets Y axis at (0 ,4) which is calculated by substituting x = 0 in Equation 1. Let this Coordinate name be P2 Equation 2 meets Y axis at (0 , – 1) which is calculated by substituting x = 0 in Equation 2. Let this Coordinate name be P3 So Area of the triangle =  1 2 12 x | x1 x (y2 – y3) + x2 x (y3 – y1) + x3 x (y1 – y2) | Where x1 ,y1 are the coordinates of P1 x2, y2 are the coordinates of P2 x3 ,y3 are the coordinates of P3 ⇒ Area of the Given Triangle =  1 2 12 x | 3 x (4 +1) + 0 x ( – 1 – 2) + 0 x (2– 4) | ⇒ Area of the Given Triangle =  1 2 12 x | 3  1 2 12 5 | ⇒ Area =  15 2 152 ⇒ Area = 7.5 Sq. Units Area of the triangle is 7.5 sq.

And in this photo answer is correct and easy solution

well done

Thankyou..