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Solve the following system of equations graphically:
$x\ β\ 2y\ =\ 6$
$3x\ β\ 6y\ =\ 0$
Given:
The given system of equations is:
$x\ –\ 2y\ =\ 6$
$3x\ –\ 6y\ =\ 0$
To do:
We have to represent the above system of equations graphically.
Solution:
The given pair of equations are:
$x\ -\ 2y\ -\ 6\ =\ 0$....(i)
$2y=x-6$
$y=\frac{x-6}{2}$
$3x\ -\ 6y\ =\ 0$....(ii)
$6y=3x$
$y=\frac{3x}{6}$
$y=\frac{x}{2}$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=2$ then $y=\frac{2-6}{2}=\frac{-4}{2}=-2$
If $x=0$ then $y=\frac{0-6}{2}=\frac{-6}{2}=-3$
| $x$ | $2$ | $0$ |
$y=\frac{x-6}{2}$ | $-2$ | $-3$ |
For equation (ii),
If $x=0$ then $y=\frac{0}{2}=0$
If $x=2$ then $y=\frac{2}{2}=1$
| $x$ | $0$ | $2$ |
| $y=\frac{x}{2}$ | $0$ | $1$ |
The above situation can be plotted graphically as below:
The line AB represents the equation $x-2y-6=0$ and the line PQ represents the equation $3x-6y=0$.
Clearly, the two lines are parallel to each other.
Hence, the given system of equations has no solution.
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