Question

If ${{D}_{y}}=-15$ and $D=-5$ are the values of the determinants for certain simultaneous equations in x and y, find y.
(a) 0
(b) 1
(c) 2
(d) 3

Answer 1

Hint: We start solving the problem by recalling the Cramer’s method of solving the system of linear equations. We know that the solution of the system of linear equations as $x=\dfrac{{{D}_{x}}}{D}$ and $y=\dfrac{{{D}_{y}}}{D}$, where ${{D}_{x}}$, ${{D}_{y}}$ and $D$ are the determinants for certain simultaneous linear equations. We then substitute the value in $y=\dfrac{{{D}_{y}}}{D}$ and make the calculations to get the required value of y.

Complete step by step answer:
According to the problem, we are given that ${{D}_{y}}=-15$ and $D=-5$ are the values of the determinants for certain simultaneous equations in x and y. We need to find the value of y.
We know that in Cramer’s method of solving the system of equations in x and y, the solutions for x and y is defined as $x=\dfrac{{{D}_{x}}}{D}$ and $y=\dfrac{{{D}_{y}}}{D}$, where ${{D}_{x}}$, ${{D}_{y}}$ and $D$ are the determinants for certain simultaneous linear equations.
So, we have given that ${{D}_{y}}=-15$ and $D=-5$ to find the value of y.
We get $\dfrac{{{D}_{y}}}{D}=\dfrac{-15}{-5}$.
$\Rightarrow \dfrac{{{D}_{y}}}{D}=3$.
$\Rightarrow y=3$.
So, we have found the value of y as 3.

So, the correct answer is “Option d”.

Note: Whenever we get this type of problem, we should know that the problem involves Cramer's method of solving the system of linear equations. We should make sure that the value of determinant D is not equal to 0 before solving this problem. We can also tell whether there are unique solutions or infinite solutions or no solutions for the given system of linear equations using the values of ${{D}_{x}}$, ${{D}_{y}}$ and $D$. Similarly, we can expect problems to find the solution using matrix inversion method by giving the linear equations.