Show graphically that the system of equations `2x+4y=10` `3x+6y=12`

Explanation

The given equation is
2x + 4y = 10
implies 4y = 10 - 2x implies `y = (5-x)/(2)`
`{:(x,1,3,5),(y = (5-x)/(2),2,1,0):}`
Now for equation 3x + 6y = 12
implies 6y = 12 - 3x implies `y = (4-x)/(2)`
`{:(x,2,0,4),(y = (4-x)/(2),1,2,0):}`
Now plot the points A(1, 2), B(3, 1), C(5, 0) and P(2, 1), Q(0, 2), R(4, 0) on the same graph paper.

We observe from the graph that the two lines are parallel to each other i.e., they do not intersect each other at any point. Hence, the given system of equation has no solution.
Hence Proved.