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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:
$x\ +\ 2y\ =\ 5$$2x\ -\ 3y\ =\ -4$
Given:
The given system of equations is:
$x\ +\ 2y\ =\ 5$
$2x\ -\ 3y\ =\ -4$
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:
$x+2y-5=0$....(i)
$2y=5-x$
$y=\frac{5-x}{2}$
$2x-3y+4=0$.....(ii)
$3y=2x+4$
$y=\frac{2x+4}{3}$
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation (i),
If $x=5$ then $y=\frac{5-5}{2}=\frac{0}{2}=0$
If $x=1$ then $y=\frac{5-1}{2}=\frac{4}{2}=2$
$x$ | $5$ | $1$ |
$y$ | $0$ | $2$ |
For equation (ii),
If $x=-2$ then $y=\frac{2(-2)+4}{3}=\frac{-4+4}{3}=\frac{0}{3}=0$
If $x=1$ then $y=\frac{2(1)+4}{3}=\frac{2+4}{3}=\frac{6}{3}=2$
$x$ | $-2$ | $1$ |
| $y$ | $0$ | $2$ |
The above situation can be plotted graphically as below:
The lines AB and CD represent the equations $x+2y=5$ and $2x-3y=-4$.
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 $x=1$ and $y=2$. The lines represented by the equations $x+2y=5$ and $2x-3y=-4$ meet X-axis at $(5,0)$ and $(-2,0)$ respectively.
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