Solve graphically the following system of linear equations. Also find the coordinates of the points where the lines meet axis of y.

$2x\ +\ y\ -\ 11\ =\ 0$
$x\ -\ y\ -\ 1\ =\ 0$

Given:

The given system of equations is:

$2x\ +\ y\ -\ 11\ =\ 0$

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

To do:

We have to solve the given system of equations and find the coordinates of the points where the lines meet axis of y.

Solution:

The given pair of equations is:

$2x\ +\ y\ -\ 11\ =\ 0$....(i)

$y=11-2x$

$x-y-1=0$.....(ii)

$y=x-1$

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

For equation (i),

If $x=5$ then $y=11-2(5)=11-10=1$

If $x=4$ then $y=11-2(4)=11-8=3$

For equation (ii),

If $x=1$ then $y=1-1=0$

If $x=4$ then $y=4-1=3$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $2x+y-11=0$ and $x-y-1=0$.

The solution of the given system of equations is the intersection point of the lines AB and CD and these lines meet Y-axis at points E and F respectively.

Hence, the solution of the given system of equations is $x=4$ and $y=3$. The lines represented by the equations $2x+2y-11=0$ and $x-y-1=0$ meet Y-axis at $(0,11)$ and $(0,-1)$ respectively.

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Updated on: 10-Oct-2022

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