Equations

Algebra Level 2
  • Find the value of a a such that the pair of linear equations are inconsistent.
  • 2 x + 3 y = 5 2x+3y=5
  • a x + 6 y = 12 ax+6y=12
5 6 4 1

Vishwathiga Jayasankar by vishwathiga jayasankar , 20, India

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2 solutions

Viki Zeta
Oct 4, 2016

a 1 a 2 = b 1 b 2 ≠ c 1 c 2 2 a = 3 6 ≠ 5 12 Equating first 2 expression 2 a = 3 6 a = 2 × 6 3 = 4 Equating first and last 2 a ≠ 5 12 a ≠ 12 × 2 5 a ≠ 4.8 ⟹ a = 4 ∴ a = 4 \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\ne\dfrac{c_1}{c_2} \\ \dfrac{2}{a} = \dfrac{3}{6} \ne \dfrac{5}{12} \\ \text{Equating first 2 expression} \\ \dfrac{2}{a} = \dfrac{3}{6} \\ a = \dfrac{2\times6}{3} = 4 \\ \text{Equating first and last} \\ \dfrac{2}{a} \ne \dfrac{5}{12} \\ a \ne \dfrac{12 \times 2}{5} \\ a \ne 4.8\\ \implies a = 4\\ \boxed{\therefore a = 4}

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  • For equations to be inconsistent:
  • a 1 a 2 \frac{a1}{a2} = b 1 b 2 \frac{b1}{b2} should not be= c 1 c 2 \frac{c1}{c2}
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