On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x - axis and the y- axis respectively.
Graph of ` 2x - 3y = 5 `
` 2x - 3y = 5 rArr 3y = ( 2x - 5) `
`" " rArr y = (( 2x - 5))/(3)" "` ... (i)
Putting ` x = - 2 `in (i), we get ` y = - 3 `
Putting ` x = 1 ` in (i), we get ` y = - 1 `
Putting ` x = 4 ` in (i), we get ` y = 1 `
Thus, we have the following table for the equation ` 2x - 3y = 5`
Now, plot the points `A(-2, - 3), B(1, - 1 ) and C(4, 1)` on the graph paper.
Join AB and BC to get the graph line ABC. Extendj it on both ways.
Thus, the line ABC is the graph of the equation ` 2x - 3y = 5 `
Graph of ` 6y- 4x = 3 `
` 6y - 4x = 3 rArr 6y = ( 3 + 4x )`
` " " rArr y = (( 3 + 4x ))/( 6)" "` ... (ii)
Putting ` x = - 3 ` in (ii), we get `y = (-3)/(2)`
Putting ` x = 0 ` in (ii), we get ` y = (1)/(2)`.
Putting ` x = 3 ` in (ii), we get ` y = (5)/(2)`.
Thus, we have the following table for the equation ` 6y - 4x = 3 `.
Now, plot the points `P(-3, (-3)/(2)), Q(0, (1)/(2)) and R ( 3, (5)/(2))` on the same graph paper as above . join PQ and QR to get the graph line PQR. Extend it on both ways.
Then, the line PQR is the graph of the equation ` 6y - 4x = 3`.
It is clear from the graph that the two graph lines are parallel and do not interest even when produced.
Hence, the given system of equations has no solution.
