Finding ratios (Consistency)

Chapter 3 Class 10 Pair of Linear Equations in Two Variables
Concept wise

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### Transcript

Ex 3.1, 2 On comparing the ratios π1/π2 , π1/π2 & π1/π2 , find out whether the lines representing the following pair of linear equations intersect at a point, parallel or coincident 5x β 4y + 8 = 0 ; 7x + 6y β 9 = 0 5x β 4y + 8 = 0 7x + 6y β 9 = 0 5x β 4y + 8 = 0 Comparing with a1x + b1y + c1 = 0 β΄ a1 = 5 , b1 = β4 , c1 = 8 7x + 6y β 9 = 0 Comparing with a2x + b2y + c2 = 0 β΄ a2 = 7 , b2 = 6 , c2 = β9 β΄ a1 = 5 , b1 = β4 , c1 = 8 & a2 = 7 , b2 = 6 , c2 = β9 ππ/ππ π1/π2 = 5/7 ππ/ππ π1/π2 = (β4)/6 π1/π2 = (β2)/3 ππ/ππ π1/π2 = 8/(β9) π1/π2 = (β8)/9 Since π1/π2 β  π1/π2 So, have unique solution Therefore, the lines that represent the linear equations intersect at a point