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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\ =\ 6$$x\ -\ 2y\ =\ -2$
Given:
The given system of equations is:
$2x\ +\ y\ =\ 6$
$x\ -\ 2y\ =\ -2$
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:
$2x+y-6=0$....(i)
$y=6-2x$
$x-2y+2=0$.....(ii)
$2y=x+2$
$y=\frac{x+2}{2}$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=3$ then $y=6-2(3)=6-6=0$
If $x=2$ then $y=6-2(2)=6-4=2$
$x$ | $3$ | $2$ |
$y$ | $0$ | $2$ |
For equation (ii),
If $x=-2$ then $y=\frac{-2+2}{2}=\frac{0}{2}=0$
If $x=2$ then $y=\frac{2+2}{2}=\frac{4}{2}=2$
$x$ | $-2$ | $2$ |
| $y$ | $0$ | $2$ |
The above situation can be plotted graphically as below:
The lines AB and CD represent the equations $2x+y=6$ and $x-2y=-2$.
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 $x=2$ and $y=2$. The lines represented by the equations $2x+y=6$ and $x-2y=-2$ meet X-axis at $(3,0)$ and $(-2,0)$ respectively.
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