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Question

Check whether the following pair of equation is consistent.
3x+4y=2 and 6x+8y=4. Verify by a graphical representation.

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Solution

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 a1a2b1b2 or a1a2=b1b2=c1c2

Now, the given equations are,

3x+4y=23x+4y2=0

6x+8y=46x+8y4=0

Here, 36=48=24=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.


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