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On comparing the ratios a1a2,b1b2 and c1c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x−4y+8=0;7x+6y−9=0?
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On comparing the ratios a1a2,b1b2 and c1c2, find out whether the lines...

Comparison of Ratios

To determine whether the lines represented by the pair of linear equations intersect at a point, are parallel, or coincident, we can compare the ratios of coefficients in the equations.

Given Equations:
1. 5x - 4y + 8 = 0
2. 7x + 6y - 9 = 0

Calculation of Ratios:
- Ratio a1/a2 = 5/7
- Ratio b1/b2 = -4/6 = -2/3
- Ratio c1/c2 = 8/-9 = -8/9

Analysis:
- Since the ratios a1/a2, b1/b2, and c1/c2 are not equal, the lines represented by the given pair of linear equations will intersect at a point. This means that the lines are not parallel or coincident.

Therefore, the lines represented by the equations 5x - 4y + 8 = 0 and 7x + 6y - 9 = 0 will intersect at a unique point.
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On comparing the ratios a1a2,b1b2 and c1c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident. 5x−4y+8=0;7x+6y−9=0?
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