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

$3x\ +\ y\ -\ 5\ =\ 0$
$2x\ -\ y\ -\ 5\ =\ 0$

Given:

The given system of equations is:

$3x\ +\ y\ -\ 5\ =\ 0$

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

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:

$3x\ +\ y\ -\ 5\ =\ 0$....(i)

$y=5-3x$

$2x-y-5=0$.....(ii)

$y=2x-5$

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

For equation (i),

If $x=1$ then $y=5-3(1)=5-3=2$

If $x=2$ then $y=5-3(2)=5-6=-1$

For equation (ii),

If $x=2$ then $y=2(2)-5=4-5=-1$

If $x=3$ then $y=2(3)-5=6-5=1$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $3x+y-5=0$ and $2x-y-5=0$.

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 $x=2$ and $y=-1$. The lines represented by the equations $3x+y-5=0$ and $2x-y-5=0$ meet Y-axis at $(0,5)$ and $(0,-5)$ respectively.

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Updated on: 10-Oct-2022

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