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


$2x\ -\ 5y\ +\ 4\ =\ 0$
$2x\ +\ y\ -\ 8\ =\ 0$

Given:

The given system of equations is:

$2x\ -\ 5y\ +\ 4\ =\ 0$

$2x\ +\ y\ -\ 8\ =\ 0$

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:

$2x\ -\ 5y\ +\ 4\ =\ 0$....(i)

$5y=2x+4$

$y=\frac{2x+4}{5}$

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

$y=8-2x$

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

For equation (i),

If $x=-2$ then $y=\frac{2(-2)+4}{5}=\frac{-4+4}{5}=0$

If $x=3$ then $y=\frac{2(3)+4}{5}=\frac{6+4}{5}=\frac{10}{5}=2$

For equation (ii),

If $x=4$ then $y=8-2(4)=8-8=0$

If $x=3$ then $y=8-2(3)=8-6=2$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $2x-5y+4=0$ and $2x+y-8=0$.

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 F and E respectively.

Hence, the solution of the given system of equations is $x=3$ and $y=2$. The lines represented by the equations $2x-5y+4=0$ and $2x+y-8=0$ meet Y-axis at $(0,\frac{4}{5})$ and $(0,8)$ respectively.

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Updated on: 10-Oct-2022

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