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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.
$2x\ -\ 5y\ +\ 4\ =\ 0$
$2x\ +\ y\ -\ 8\ =\ 0$
Given:
The given system of equations is:
$2x\ -\ 5y\ +\ 4\ =\ 0$
$2x\ +\ y\ -\ 8\ =\ 0$
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:
$2x\ -\ 5y\ +\ 4\ =\ 0$....(i)
$5y=2x+4$
$y=\frac{2x+4}{5}$
$2x+y-8=0$.....(ii)
$y=8-2x$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=-2$ then $y=\frac{2(-2)+4}{5}=\frac{-4+4}{5}=0$
If $x=3$ then $y=\frac{2(3)+4}{5}=\frac{6+4}{5}=\frac{10}{5}=2$
$x$ | $-2$ | $3$ |
$y=\frac{2x+4}{5}$ | $0$ | $2$ |
For equation (ii),
If $x=4$ then $y=8-2(4)=8-8=0$
If $x=3$ then $y=8-2(3)=8-6=2$
$x$ | $4$ | $3$ |
$y=8-2x$ | $0$ | $2$ |
The above situation can be plotted graphically as below:
The lines AB and CD represent the equations $2x-5y+4=0$ and $2x+y-8=0$.
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 F and E respectively.
Hence, the solution of the given system of equations is $x=3$ and $y=2$. The lines represented by the equations $2x-5y+4=0$ and $2x+y-8=0$ meet Y-axis at $(0,\frac{4}{5})$ and $(0,8)$ respectively.