Solve the following system of equations graphically:
$x\ +\ y\ =\ 4$
$2x\ –\ 3y\ =\ 3$

Given:

The given system of equations is:

$x\ +\ y\ =\ 4$

$2x\ –\ 3y\ =\ 3$

To do:

We have to represent the above system of equations graphically.

Solution:

The given pair of equations are:

$x\ +\ y\ -\ 4\ =\ 0$....(i)

$y=4-x$

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

$3y=2x-3$

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

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

For equation (i),

If $x=0$ then $y=4-0=4$

If $x=4$ then $y=4-4=0$

$x$	$0$	$4$
$y=4-x$	$4$	$0$

For equation (ii),

If $x=0$ then $y=\frac{2(0)-3}{3}=\frac{-3}{3}=-1$

If $x=3$ then $y=\frac{2(3)-3}{3}=\frac{6-3}{3}=\frac{3}{3}=1$

$x$	$0$	$3$
$y=\frac{2x-3}{3}$	$-1$	$1$

The above situation can be plotted graphically as below:

The line AB represents the equation $x+y-4=0$ and the line PQ represents the equation $2x-3y-3=0$.

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

Hence, the solution of the given system of equations is $x=3$ and $y=1$.

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Updated on: 10-Oct-2022

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Solve the following system of equations graphically:$x\ +\ y\ =\ 4$$2x\ –\ 3y\ =\ 3$