Solve the following system of equations graphically:
$2x\ +\ y\ –\ 3\ =\ 0$
$2x\ –\ 3y\ –\ 7\ =\ 0$

Given:

The given system of equations is:

$2x\ +\ y\ –\ 3\ =\ 0$

$2x\ –\ 3y\ –\ 7\ =\ 0$

To do:

We have to represent the above system of equations graphically.

Solution:

The given pair of equations are:

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

$y=3-2x$

$2x\ -\ 3y\ -\ 7\ =\ 0$....(ii)

$3y=2x-7$

$y=\frac{2x-7}{3}$

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

For equation (i),

If $x=0$ then $y=3-2(0)=3-0=3$

If $x=1$ then $y=3-2(1)=3-2=1$

For equation (ii),

If $x=2$ then $y=\frac{2(2)-7}{3}=\frac{4-7}{3}=\frac{-3}{3}=-1$

If $x=5$ then $y=\frac{2(5)-7}{3}=\frac{10-7}{3}=\frac{3}{3}=1$

The above situation can be plotted graphically as below:

The line AB represents the equation $2x+y-3=0$ and the line PQ represents the equation $2x-3y-7=0$.

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 $x=2$ and $y=-1$.

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Updated on: 10-Oct-2022

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