Math, asked by vaishalidongre2270, 4 months ago

draw a graph representing the equation x-y=1 and 2x+3y=12 on the same graph paper . Find the area of triangles formed by these lines the x axis and y axis

Answers

Answered by BlessOFLove

Graph of the equation 2x + 3y - 12 = 0

we have,

$2x &#x2b; 3y = 12 =$

2x = 12 - 3y =

→ `x = (12- 3y )/ 2°

Putting y = 4, we get `x ( 12 - 3 xx 4)/2 = 0

Putting y = 2, we get `x = (12 - 3 xx = =4)/2= 0

Thus, we have the following table for the p table for the points on the line 2x + 3y = 12

⠀⠀⠀⠀⠀⠀⠀ $\{\fcolorbox{red}{pink}{x}$ $\{\fcolorbox{red}{pink}{0}$ $\{\fcolorbox{yellow}{green}{3}$

⠀⠀⠀⠀⠀⠀⠀ $\{\fcolorbox{green}{red}{y}$ $\{\fbox{4}$ $\{\fbox{2}$

Plotting points A ( 0,4 ) , B (3,2) on the graph paper and drawing a line

passing through them

we obtain graph of the equation.

Graph of the equation

Graph of the equation x-y - 1 :

We have x $&#x2212$ $&#x3d$ y = 1 = x = 1 $&#x2b$ y

Thus, we have the following table for the points the line x - y = 1

⠀⠀⠀⠀⠀⠀⠀ $\{\fcolorbox{red}{pink}{x}$ $\{\fcolorbox{red}{pink}{1}$ $\{\fcolorbox{yellow}{green}{0}$

⠀⠀⠀⠀⠀⠀⠀ $\{\fcolorbox{green}{red}{y}$ $\{\fbox{0}$ $\{\fbox{-1}$

Plotting points C(1,0) and D (0,-1) on the same graph paper drawing a line passing through

the m, we obtain the graph of the line represents by the equation x - y = 1

Clearly two lines intersect at A (3, 2)

The graph of time 2x + 3y = 12 = intersect with y-axis at B (0,4) and the graph of the line

X - y = 1 intersect with y axis at c ( =

0,-1).

So, the vertices of the triangle formed by thee two straight lines and y-axis are A (3,2) and

B( 0.4) and C (0,-1)

Now,

Area of `AABC = 1/2` [ Base xx =

Height]

= 1/2 ( Bc xx AB)` =

= 1/2 ( 5 + 3)`

= 15/2 sq .units

Attachments:

Answered by AlphaRone

Answer:

Step-by-step explanation:

Graph of the equation 2x + 3y - 12 = 0