Question

Show graphically that each of the following given systems of equations is inconsistent.i.e., has no solution:

$2x+3y=4,4x+6y=12.$

Answer 1

Given equations are
$2x+3y=4and4x+6y=12$

Graph of $2x+3y=4:$

$2x+3y=4$

$\Rightarrow y=\frac{(-2x+4)}{3}$

Putting x = 2, we get y = 2

Putting x = -1, we get y = 2

Putting x = -4, we get y = 4

Hence, the table is,

x	2	-1	-4
y	0	2	4

Plot the points A(2, 0), B(-1, 2) and C(-4, 4) on the graph paper. Join AB and BC to get the graph line AC. Extend it both ways.

Thus, line AC is the graph of $2x+3y=4.$

Graph of $4x+6y=12:$

$4x+6y=12$

$\Rightarrow y=\frac{(-4x+12)}{6}$

Putting x = 3, we get y = 0

Putting x = 0, we get y = 2

Putting x = 6, we get y = -2

Hence, the table is,

x	3	0	6
y	0	2	-2

Now, on the same graph paper as above plot the points P(3, 0) and Q(0, 2) and R(6, -2). Join PQ and PR to get QR.

Thus, line QR is the graph of $4x+6y=12.$

It is not clear from the graph that the two graph lines are parallel and do not intersect when produced.

Hence, the given system of equation is consistent.