Check whether the following pair of equation is consistent.
3x+4y=2 and 6x+8y=4. Verify by a graphical representation.
If two lines consistent then lines may be intersect or coincided to each other.
If the line a1x+b1y+c1=0 and a2x+b2y+c2=0 are consistent then,
either a1a2≠b1b2 or a1a2=b1b2=c1c2
Now, the given equations are,
3x+4y=2⇒3x+4y−2=0
6x+8y=4⇒6x+8y−4=0
Here, 36=48=−2−4=12
Hence, the given lines are consistent. (Coincided).
Lets draw the graph,
3x+4y=2
Put x=0
⇒3(0)+4y=2
⇒4y=2
⇒y=12
⇒(x,y)=(0,12)
Put, y=0
3x+4y=2
⇒3x+4(0)=2
⇒3x=2
⇒x=23
⇒(x,y)=(23,0)
Therefore, the plot points of the line 3x+4y=2 are (0,12) and (23,0).
Similarly, we get the same plot points for 6x+8y=4 by taking the values of x=0 and y=0.
From the graph, both lines are coincided.
Hence, the given lines are consistent.