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Solve graphically the following system of linear equations. Also find the coordinates of the points where the lines meet axis of y.
$2x\ -\ y\ -\ 5\ =\ 0$
$x\ -\ y\ -\ 3\ =\ 0$
Given:
The given system of equations is:
$2x\ -\ y\ -\ 5\ =\ 0$
$x\ -\ y\ -\ 3\ =\ 0$
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:
$2x\ -\ y\ -\ 5\ =\ 0$....(i)
$y=2x-5$
$x-y-3=0$.....(ii)
$y=x-3$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=3$ then $y=2(3)-5=6-5=1$
If $x=2$ then $y=2(2)-5=4-5=-1$
$x$ | $3$ | $2$ |
$y=2x-5$ | $1$ | $-1$ |
For equation (ii),
If $x=3$ then $y=3-3=0$
If $x=2$ then $y=2-3=-1$
$x$ | $3$ | $2$ |
| $y=x-3$ | $0$ | $-1$ |
The above situation can be plotted graphically as below:
The lines AB and CD represent the equations $2x-y-5=0$ and $x-y-3=0$.
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 $2x-y-5=0$ and $x-y-3=0$ meet Y-axis at $(0,-5)$ and $(0,-3)$ respectively.
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