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5. If two lines intersect each other, then they are not parallel. Therefore their slopes should not be same.
The slope of the line is,
And the slope of the line is,
For the two lines intersect each other,
Hence,
6. For the two lines being coincident, the two equations should be the same.
Given equations are,
Multiplying (2) by 4,
And on comparing LHS of (1) and (3), since RHS are same,
And,
7. (i) For a unique solution, the lines represented by these two equations should not be parallel, hence their slopes should not be same.
The slope of the line is,
And that of is,
Then we have,
Therefore,
7. (ii) For the system would have infinite no. of solutions because the lines become coincident. Therefore there are no values for k, for the system having no solution.
8. (i) For no solutions, the lines represented by these two lines should be parallel to each other, hence their slopes should be same.
The slope of the line is,
And that of the line is,
For the two being parallel,
The reason for here is given below.
8. (ii) For infinite solutions, the lines should be coincident. Hence the equations should be the same.
The equations are,
Multiplying (1) by 2,
And on comparing (2) and (3), we get,
I.e., the system has no solutions only if And the system has infinite solutions only if
Answer:
5. If two lines intersect each other, then they are not parallel. Therefore their slopes should not be same.
5. If two lines intersect each other, then they are not parallel. Therefore their slopes should not be same.The slope of the line 4x+py+8=04x+py+8=0 is,
And the slope of the line
For the two lines intersect each other,
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