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DSSSB TGT Maths Female Subject Concerned - 22 Sep 2018 Shift 2

Option 3 : -12

__ Concept:__

- If a system has no solution, it is said to be inconsistent.
- For a system of equations having no solution,

a1 x + b1 y = c1 and a2 x + b2 y = c2

\(\text{we have}, \dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}≠ \dfrac{c_{1}}{c_{2}}\)

**Calculation:**

The given equations are 2x - 3y - 3 = 0 and -4x + qy - \(\dfrac{p}{2}\) = 0

So, here **on comparing **these equations with equation(1) and (2), we have

a_{1 }= 2, b_{1 }= -3, c_{1 }= -3;

a_{2} = -4, b_{2 }= q, c_{2 }= \(\dfrac{-p}{2}\)

Now, for a system to be **inconsistent**,

\(\text{we have}, \dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}≠ \dfrac{c_{1}}{c_{2}}\)

\(\Rightarrow\dfrac{2}{-4}=\dfrac{-3}{q}≠ \dfrac{-3\times 2}{-p}\)

\(⇒ \dfrac{2}{-4}≠ \dfrac{-3\times 2}{-p}\)

\(\Rightarrow p≠-12 \)

**Hence, the given system is inconsistent when** **p ≠ 12.**