Solve the following system of equations graphically:Shade the region bounded by the lines and the y-axis.
$4x\ -\ y\ =\ 4, \ 3x\ +\ 2y\ =\ 14$

 Given:

The given equations are:

$4x\ -\ y\ =\ 4, \ 3x\ +\ 2y\ =\ 14$

To do:

We have to solve the given system of linear equations and shade the region bounded by the given lines and the y-axis.

Solution:

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

For equation $4x-y=4$,

$y=4x-4$

If $x=1$ then $y=4(1)-4=4-4=0$

If $x=2$ then $y=4(2)-4=8-4=4$

For equation $3x+2y=14$,

$2y=14-3x$

$y=\frac{14-3x}{2}$

If $x=4$ then $y=\frac{14-3(4)}{2}=\frac{14-12}{2}=\frac{2}{2}=1$

If $x=2$ then $y=\frac{14-3(2)}{2}=\frac{14-6}{2}=\frac{8}{2}=4$

The equation of y-axis is $x=0$.

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $4x-y=4$ and $3x+2y=14$ respectively.

The shaded area is the region bounded by the given lines and y-axis.

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Updated on: 10-Oct-2022

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