Question

Solve graphically the following system of linear Equations (use graph sheet) x-3y=3 2x+3y=6 AlSo find out area of triangle

Answer 1

by using this draw the graph neatly in graph sheet and then you get like graph then take coordinates of the points and you will get area

I hope it helps you.

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Answer 2

The area of the triangle is $\frac{9}{2}$ square units.

Explanation:

The equations are $x-3y=3$ and $2 x+3 y=6$

Solving the two equations, we get,

$x=3$ and $y=0$

Thus, the solution of the linear equations are $(3,0)$

Now, we shall determine the x and y intercepts of the two equations.

Consider the equation $x-3y=3$

When $x=0$, $x-3y=3 \implies y=-1$ Thus, $(0,-1)$

When $y=0$, $x-3y=3 \implies x=3$ Thus, $(3,0)$

Consider the equation, $2 x+3 y=6$

When $x=0$, $2 x+3 y=6 \implies y=2$ Thus, $(0,2)$

When $y=0$, $2 x+3 y=6 \implies x=3$ Thus, $(3,0)$

These points are plotted in the graph which is attached below:

Now, we shall determine the area of the triangle using the coordinates $(0,2)$, $(3,0)$  and $(0,-1)$

The formula for area of the triangle is given by

$A=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]$

Substituting the values, we get,

$\begin{aligned} A &=\frac{1}{2}[0(0+1)+3(-1-2)+0(2+1)] \\ &=\frac{1}{2}[0+3(-3)+0] \\ &=\frac{1}{2}(-9) \\ &=-\frac{9}{2} \end{aligned}$

Since, the area cannot be negative.

Thus, the area of the triangle is $\frac{9}{2}$ square units.

Learn more:

(1) brainly.in/question/14698903

(2) brainly.in/question/3161070