Solve the following system of equations graphically:
$x\ -\ y\ +\ 1\ =\ 0$
$3x\ +\ 2y\ -\ 12\ =\ 0$

Given:

The given system of equations is:

$x\ -\ y\ +\ 1\ =\ 0$

$3x\ +\ 2y\ -\ 12\ =\ 0$

To do:

We have to represent the above system of equations graphically.

Solution:

The given pair of equations are:

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

$y=x+1$

$3x\ +\ 2y\ -\ 12\ =\ 0$....(ii)

$2y=12-3x$

$y=\frac{12-3x}{2}$

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

For equation (i),

If $x=1$ then $y=1+1=2$

If $x=2$ then $y=2+1=3$

For equation (ii),

If $x=0$ then $y=\frac{12-3(0)}{2}=\frac{12-0}{2}=\frac{12}{2}=6$

If $x=2$ then $y=\frac{12-3(2)}{2}=\frac{12-6}{2}=\frac{6}{2}=3$

The above situation can be plotted graphically as below:

The line AB represents the equation $x-y+1=0$ and the line PQ represents the equation $3x+2y-12=0$.

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 $y=3$.

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Updated on: 10-Oct-2022

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