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


$3x\ +\ 2y\ =\ 12$
$5x\ -\ 2y\ =\ 4$

Given:

The given system of equations is:

$3x\ +\ 2y\ =\ 12$

$5x\ -\ 2y\ =\ 4$

To do:

We have to solve the given system of equations and find the coordinates of the points where the lines meet axis of y.

Solution:

The given pair of equations is:

$3x\ +\ 2y\ -\ 12\ =\ 0$....(i)

$2y=12-3x$

$y=\frac{12-3x}{2}$

$5x-2y-4=0$.....(ii)

$2y=5x-4$

$y=\frac{5x-4}{2}$

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

For equation (i),

If $x=4$ then $y=\frac{12-3(4)}{2}=\frac{12-12}{2}=0$

If $x=2$ then $y=\frac{12-3(2)}{2}=\frac{12-6}{2}=\frac{6}{2}=3$

For equation (ii),

If $x=0$ then $y=\frac{5(0)-4}{2}=\frac{-4}{2}=-2$

If $x=2$ then $y=\frac{5(2)-4}{2}=\frac{10-4}{2}=\frac{6}{2}=3$

The above situation can be plotted graphically as below:

The lines AB and CD represent the equations $3x+2y=12$ and $5x-2y=4$.

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 C respectively.

Hence, the solution of the given system of equations is $x=2$ and $y=3$. The lines represented by the equations $3x+2y=12$ and $5x-2y=4$ meet Y-axis at $(0,6)$ and $(0,-2)$ respectively.

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Updated on: 10-Oct-2022

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