Solve the following system of equations graphically:Shade the region bounded by the lines and the y-axis.
$3x\ -\ 4y\ =\ 7, \ 5x\ +\ 2y\ =\ 3$

 Given:

The given equations are:

$3x\ -\ 4y\ =\ 7, \ 5x\ +\ 2y\ =\ 3$

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 $3x-4y-7=0$,

$4y=3x-7$

$y=\frac{3x-7}{4}$

If $x=5$ then $y=\frac{3(5)-7}{4}=\frac{15-7}{4}=\frac{8}{4}=2$

If $x=1$ then $y=\frac{3(1)-7}{4}=\frac{3-7}{4}=\frac{-4}{4}=-1$

For equation $5x+2y-3=0$,

$2y=3-5x$

$y=\frac{3-5x}{2}$

If $x=-1$ then $y=\frac{3-5(-1)}{2}=\frac{3+5}{2}=\frac{8}{2}=4$

If $x=1$ then $y=\frac{3-5(1)}{2}=\frac{3-5}{2}=\frac{-2}{2}=-1$

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 $3x-4y=7$ and $5x+2y=3$ respectively.

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

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Updated on: 10-Oct-2022

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