On a graph pape, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y - axis repectively.
Graph of ` x - y = 8`
The first equation is ` x - y = 8" "` ... (i)
Now, ` x - y = 8 rArr y = x - 8`.
Putting ` x = 3 ` in (i), we get ` y = - 5 `
Putting ` x = 4 ` in (i), we get ` y = - 4 `
Putting ` x = 5 ` in (i), we get `y = - 3 `.
Thus, we have the following table for the equation ` x - y = 8`.
Now, we plot the points ` A(3, - 5), B(4, - 4) and C(5, - 3)` on the graph paper. Join AB and BC to get the graph line ABC.
Graph of ` 3x - 3y = 16`
The second equation is `3x - 3y = 16`.
` 3x - 3y = 16 rArr 3y = 3x - 16 rArr y = ((3x - 16))/(3)" " ` ... (ii)
Putting ` x = 2 ` in (ii), we get `y = (-10)/(3) = - 3 (1)/(3) = - 3.3`.
Putttin ` x = 3 ` in (ii), we get ` y = (-7)/(3) = - 2 (1)/(3) = -2.3.`
Putting ` x = 0 ` in (ii), we get ` y = (-16)/( 3 ) = - 5 (1)/(3) = - 5.3`.
Thus, we have the following table for the equation ` 3x - 3y = 16`
Now , we plot ` D(3, -2.3), E(2, -3.3) and F(0, -5.3)` on the same graph paper as above.
Join DE and EF to get the graph line DEF.
It is clear from the graph that the lines ABC and DEF are parallel and do not meet when produced.
Hence, the given system of equations has no solution and therefore, it is inconsistent.
