On a graph paper, draw a horizontal line X'OX and vertical line YOY' as the x-axis and the y-axis respectively.
Graph of ` 3x - y = 2 `
` 3x - y = 2 rArr ( 3x - 2)" " `… (i)
Putting ` x = - 1 ` in (i), we get `y = - 5 `.
Putting ` x = 0` in (i), we get ` y = - 2 `
Putting ` x = 2 ` in (i), we get ` y = 4 `
Thus, we have the following table for ` 3x - y = 2 `
Now, plot the points ` A(-1, - 5), B(0, 2 ) and C(2, 4 )` on the graph paper.
Join AB and BC to get the graph line ABC.
Extend the graph line ABC on both sides.
Thus, the line ABC is the graph of the equation ` 3 x - y = 2 `
Graph of `9x - 3y = 6`
` 9x - 3y = 6 rArr 3y = (9 x - 6)`
` " " rArr y = ((9x - 6))/( 3)" " `...(ii)
Putting ` x = - 2 `in (ii), we get ` y = - 8`
Putting ` x = 1` in (ii), we get ` y = 1 `
Putting ` x =2` in (ii), we get ` y = 4`.
Thus, we have the following table for ` 9x - 3y = 6 `
Now, plote the points ` P (- 2, - 8) and Q(1, 1 )` on the same graph paper. The point `C(2, 4 )` has already been plotted.
Join PQ and QC to obtain the line PQC.
Thus, the line PQC is the graph of ` 9x - 3y = 6`
Thus, we find that the two graph lines coincide. Hence, the given system of equations has an infinite number of solutions.
