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