Question

Solve each of the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the $x-$axis:
$x-y+3=0,2x+3y-4=0$

Answer 1

$x-y+3=0$....(1)
$2x+3y-4=0$......(2)

Isolate $x$ from equation (1) and find the value of $x$ and $y$.
$x-y+3=0$
or $x=y-3$

$x$	$y$
$-3$	$0$
$-1$	$2$
$0$	$3$

Similarly, isolate $x$ from equation (2) and find the values of $x$ and $y$.
$2x+3y-4=0$
or $x=(4-3y)/2$

$x$	$y$
$2$	$0$
$-1$	$2$
$5$	$-2$

Graph:
Both the lines intersect each other at point $(-1,2)$ and $x-$ axis at $A(-3,0)$ and $D(2,0)$ Which form a triangle, $BAD$.

Now,
Find the area of triangle $BAD$:
Area of $△BAD=1/2(base\times altitude)$
$=1/2\times 5\times 2$
$=5sq.units$. Answer!