Question

Solve the following system of linear equation graphically:

$2x+3y=12;x-y=1$.Shade the area bounded by these two lines and the x-axis.

Answer 1

Step 1: Solving and analyzing the first equation to find the values for $xandy$

Consider the first equation given,

$2x+3y=12..................................\left(1\right)$

solving the first equation

$2x=12-3y$

$x=\frac{12-3y}{2}.............................\left(2\right)$,Let this be the equation of x in terms of y

Now substituting values of y as 0,1,4 in equation(2) we obtain the following x values.

$x$	$6$	$4.5$	$0$
$y$	$0$	$1$	$4$

Step 2:Solving and analyzing the second equation to find the values for $xandy$

consider the second given equation,

$x-y=1..................................\left(3\right)$

solving the equation given

$x=1+y......................................\left(4\right)$,Let this be the equation of x in terms of y

Now substituting values of y as 0,1,3 in equation(4) we obtain the following x values.

$x$	$1$	$2$	$4$
$y$	$0$	$1$	$3$

Step 3:Graphical Representation

Plotting the points obtained on the graph ,we get the graphical representation of the solution as given below:-

Hence, the shaded region between the two lines and the x-axis is a triangle with vertices $(1,0),(6,0)and(3,2)$