Ex 3.1, 3 (iv) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Ex 3.1,3 On comparing the ratios 𝑎1/𝑎2 , 𝑏1/𝑏2 & 𝑐1/𝑐2 , find out whether the following pair of linear equations are consistent, or inconsistent. (iv) 5x – 3y = 11 , −10x + 6y = −22 5x – 3y – 11 = 0 −10x + 6y + 22 = 0 5x – 3y – 11 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 5 , b1 = −3 , c1 = – 11 −10x + 6y + 22 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = − 10 , b2 = 6, c2 = 22 ∴ a1 = 5 , b1 = −3 , c1 = – 11 & a2 = − 10 , b2 = 6, c2 = 22 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 We have infinitely many solutions Therefore, our system is consistent.