The system of equations ax + 3y = 1, –12x + ay = 2 has ________ for all real values of a.

Open in App

Solution

The given system of equations are:
ax + 3y = 1 ...(i)
–12x + ay = 2 ...(ii)

Now,
$\frac{a_{1}}{a_{2}} = \frac{a}{- 12} \frac{b_{1}}{b_{2}} = \frac{3}{a} \frac{c_{1}}{c_{2}} = \frac{- 1}{- 2} = \frac{1}{2} If \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \Rightarrow \frac{a}{- 12} = \frac{3}{a} \Rightarrow a^{2} = - 36 Which is not possible for any value of a . Thus, \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} for all real values of a .$

Hence, the system of equations ax + 3y = 1, –12x + ay = 2 has a unique solution for all real values of a.

Suggest Corrections

Similar questions

a

a x + 3 y = a - 3, 12 x + a y = a

x + a y = 0

y + a z = 0

z + a x = 0

^{'} a^{'}

x^{2} + a x + 1 = 0

a

a

3 x + a y = 3, a x + 3 y = 3

Join BYJU'S Learning Program