Solve the following system of equations graphically:
$x\ –\ 2y\ =\ 5$
$2x\ +\ 3y\ =\ 10$

Given:

The given system of equations is:

$x\ –\ 2y\ =\ 5$

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

To do:

We have to represent the above system of equations graphically.

Solution:

The given pair of equations are:

$x\ -\ 2y\ -\ 5\ =\ 0$....(i)

$2y=x-5$

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

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

$3y=10-2x$

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

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

For equation (i),

If $x=5$ then $y=\frac{5-5}{2}=0$

If $x=1$ then $y=\frac{1-5}{2}=\frac{-4}{2}=-2$

For equation (ii),

If $x=5$ then $y=\frac{10-2(5)}{3}=\frac{10-10}{3}=0$

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

The above situation can be plotted graphically as below:

The line AB represents the equation $x-2y-5=0$ and the line PQ represents the equation $2x+3y-10=0$.

The solution of the given system of equations is the intersecting point of both the lines.

Hence, the solution of the given system of equations is $x=5$ and $y=0$.

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Updated on: 10-Oct-2022

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