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On comparing the ratios a_{1}/a_{2} * b_{1}/b_{2} * an * d * c_{1}/c_{2} find out whether the lines representing thepe following pairs of linear equations intersect at a point, are parallel or coincident: 5x-4y+8-0 6/3/24" 7x + 6x - 9 = 0 )9x+3y+12-018x + 6x + 24 = 0 (3) 6x - 3y + 10 = 0?
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On comparing the ratios a_{1}/a_{2} * b_{1}/b_{2} * an * d * c_{1}/c_{...

Analysis of the given pairs of linear equations:

Pair 1:
5x - 4y + 8 = 0
6x + 3y - 24 = 0

Ratio of coefficients:
a1/a2 = 5/6
b1/b2 = -4/3
c1/c2 = 8/-24

Product of ratios:
(5/6) * (-4/3) * (8/-24) = (-10/9)

Conclusion:
Since the product of the ratios is not equal to 1, the lines represented by the given pair of linear equations intersect at a point.

Pair 2:
7x + 6y - 9 = 0
9x + 3y + 12 = 0

Ratio of coefficients:
a1/a2 = 7/9
b1/b2 = 6/3
c1/c2 = -9/12

Product of ratios:
(7/9) * (6/3) * (-9/12) = -14

Conclusion:
Since the product of the ratios is not equal to 1, the lines represented by the given pair of linear equations intersect at a point.

Pair 3:
18x + 6y + 24 = 0
6x - 3y + 10 = 0

Ratio of coefficients:
a1/a2 = 18/6
b1/b2 = 6/-3
c1/c2 = 24/10

Product of ratios:
(18/6) * (6/-3) * (24/10) = -24

Conclusion:
Since the product of the ratios is not equal to 1, the lines represented by the given pair of linear equations intersect at a point.
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On comparing the ratios a_{1}/a_{2} * b_{1}/b_{2} * an * d * c_{1}/c_{2} find out whether the lines representing thepe following pairs of linear equations intersect at a point, are parallel or coincident: 5x-4y+8-0 6/3/24" 7x + 6x - 9 = 0 )9x+3y+12-018x + 6x + 24 = 0 (3) 6x - 3y + 10 = 0?
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