Question

In the following question, a is a real number. Question: what choice of a would yield a system of linear equations with NO solutions?

9x-14y=-3

2x-ay=-6

Answer 1

Answer: The value of a should be 3.11.

Step-by-step explanation:

Since we have given that

$9x-14y=-3\\\\2x-ay=-6$

We need to find the value of a so that it would yield a system of linear equations with NO solutions.

As we know the condition of no solutions, it means the lines should be parallel.

i.e.

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$

Consider the first two terms:

$\dfrac{9}{2}=\dfrac{-14}{-a}\\\\a=\dfrac{2\times 14}{9}\\\\a=3.11$

So, the value of a should be 3.11.