Solve graphically the following system of linear equations. Also find the coordinates of the points where the lines meet axis of y.

$x\ +\ 2y\ -\ 7\ =\ 0$
$2x\ -\ y\ -\ 4\ =\ 0$

Given:

The given system of equations is:

$x\ +\ 2y\ -\ 7\ =\ 0$

$2x\ -\ y\ -\ 4\ =\ 0$

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:

$x\ +\ 2y\ -\ 7\ =\ 0$....(i)

$2y=7-x$

$y=\frac{7-x}{2}$

$2x-y-4=0$.....(ii)

$y=2x-4$

To represent the above equations graphically we need at least two solutions for each of the equations.

For equation (i),

If $x=5$ then $y=\frac{7-5}{2}=\frac{2}{2}=1$

If $x=3$ then $y=\frac{7-3}{2}=\frac{4}{2}=2$

For equation (ii),

If $x=2$ then $y=2(2)-4=4-4=0$

If $x=3$ then $y=2(3)-4=6-4=2$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $x+2y-7=0$ and $2x-y-4=0$.

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 E and F respectively.

Hence, the solution of the given system of equations is $x=3$ and $y=2$. The lines represented by the equations $x+2y-7=0$ and $2x-y-4=0$ meet Y-axis at $(0,\frac{7}{2})$ and $(0,-4)$ respectively.

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Updated on: 10-Oct-2022

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