Mathematics

On comparing the ratios $\dfrac{a$ find out whether the following pair of linear equations are consistent, or inconsistent.
$\dfrac{3}{2}x + \dfrac{5}{3}y = 7$ ; 9x - 10y = 14

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Given,

Equations : $\dfrac{3}{2}x + \dfrac{5}{3}y = 7$ ; 9x - 10y = 14 or,

$\Rightarrow \dfrac{9x + 10y}{6} = 7$ ; 9x - 10y = 14 or,

⇒ 9x + 10y = 42; 9x - 10y = 14 or,

⇒ 9x + 10y - 42 = 0; 9x - 10y - 14 = 0.

Comparing equations 9x + 10y - 42 = 0 and 9x - 10y - 14 = 0 with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 respectively, we get :

a₁ = 9, b₁ = 10, c₁ = -42, a₂ = 9, b₂ = -10 and c₂ = -14.

$\dfrac{a$

$\dfrac{b$

Since, $\dfrac{a$ ≠ $\dfrac{b$ .

Hence, the set of linear equations are consistent.

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