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Graphically, the following pair of linear equations represent two lines which are
6𝑥 − 3𝑦 + 10 = 0
2𝑥 − 𝑦 + 9 = 0

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Intersecting at exactly one point

Intersecting at exactly two points

Coincident

Parallel

answer is D.

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Detailed Solution

The given equations are

6𝑥 − 3𝑦 + 10 = 0

2𝑥 − 𝑦 + 9 = 0

Dividing both sides of eq(1) by 3, we get

2x - y + 10/3 =0

Table for above equation

x	0	-9/2
y	9	0

table for equation 2x - y + 9 = 0

x	0	-5/3
y	10/3	0

So, the graph of these equations is:

The graph clearly shows that the two lines are parallel to each other. Hence, the correct option is (d) parallel.

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