Solve the following system of equations graphically:
$3x\ +\ y\ +\ 1\ =\ 0$ 
$2x\ –\ 3y\ +\ 8\ =\ 0$

Given:

The given system of equations is:

$3x\ +\ y\ +\ 1\ =\ 0$ 

$2x\ –\ 3y\ +\ 8\ =\ 0$

To do:

We have to represent the above system of equations graphically.

Solution:

The given pair of equations are:

$3x\ +\ y\ +\ 1\ =\ 0$....(i)

$y=-3x-1$

$2x\ -\ 3y\ +\ 8\ =\ 0$....(ii)

$3y=2x+8$

$y=\frac{2x+8}{3}$

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

For equation (i),

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

If $x=0$ then $y=-3(0)-1=0-1=-1$

For equation (ii),

If $x=-1$ then $y=\frac{2(-1)+8}{3}=\frac{-2+8}{3}=\frac{6}{3}=2$

If $x=-4$ then $y=\frac{2(-4)+8}{3}=\frac{-8+8}{3}=\frac{0}{3}=0$

The above situation can be plotted graphically as below:

The line AB represents the equation $3x+y+1=0$ and the line PQ represents the equation $2x-3y+8=0$.

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

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Updated on: 10-Oct-2022

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