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Solve graphically the following system of linear equations. Also, find the coordinates of the points where the lines meet the axis of x:
$2x\ -\ y\ =\ 2$$4x\ -\ y\ =\ 8$
Given:
The given system of equations is:
$2x\ -\ y\ =\ 2$
$4x\ -\ y\ =\ 8$
To do:
We have to solve the given system of equations and find the coordinates of the points where the lines meet axis of x.
Solution:
The given pair of equations is:
$2x-y-2=0$....(i)
$y=2x-2$
$4x-y-8=0$.....(ii)
$y=4x-8$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=1$ then $y=2(1)-2=2-2=0$
If $x=3$ then $y=2(3)-2=6-2=4$
$x$ | $1$ | $3$ |
$y$ | $0$ | $4$ |
For equation (ii),
If $x=2$ then $y=4(2)-8=8-8=0$
If $x=3$ then $y=4(3)-8=12-8=4$
$x$ | $2$ | $3$ |
| $y$ | $0$ | $4$ |
The above situation can be plotted graphically as below:
The lines AB and CD represent the equations $2x-y=2$ and $4x-y=8$.
The solution of the given system of equations is the intersection point of the lines AB and CD and these lines meet X-axis at points A and C respectively.
Hence, the solution of the given system of equations is $x=3$ and $y=4$. The lines represented by the equations $2x-y=2$ and $4x-y=8$ meet X-axis at $(1,0)$ and $(2,0)$ respectively.
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