Solve the following system of linear equations graphically and shade the region between the two lines and x-axis:

$3x\ +\ 2y\ -\ 11\ =\ 0$
$2x\ -\ 3y\ +\ 10\ =\ 0$

Given:

The given system of equations is:

$3x\ +\ 2y\ -\ 11\ =\ 0$

$2x\ -\ 3y\ +\ 10\ =\ 0$

 To do:

We have to solve the given system of equations and shade the region between the two lines and x-axis.

Solution:

The given pair of equations is:

$3x\ +\ 2y\ -\ 11\ =\ 0$....(i)

$2y=11-3x$

$y=\frac{11-3x}{2}$

$2x-3y+10=0$.....(ii)

$3y=2x+10$

$y=\frac{2x+10}{3}$

To represent the above equations graphically we need at least two solutions for each of the equations.

For equation (i),

If $x=3$ then $y=\frac{11-3(3)}{2}=\frac{11-9}{2}=\frac{2}{2}=1$

If $x=1$ then $y=\frac{11-3(1)}{2}=\frac{11-3}{2}=\frac{8}{2}=4$

For equation (ii),

If $x=-2$ then $y=\frac{2(-2)+10}{3}=\frac{-4+10}{3}=\frac{6}{3}=2$

If $x=1$ then $y=\frac{2(1)+10}{3}=\frac{2+10}{3}=\frac{12}{3}=4$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $3x+2y-11=0$ and $2x-3y+10=0$.

The solution of the given system of equations is the intersection point of the lines AB and CD.

Hence, the solution of the given system of equations is $x=1$ and $y=4$.

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Updated on: 10-Oct-2022

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