Question

Solve the following system of equations-
$
  \sqrt 2 x - \sqrt 3 y = 0 \\
    \\
  \sqrt 3 x - \sqrt 8 y = 0 \\
$

Answer 1

Hint- We will use the method of substitution after finding out the value of x using the equations given in the question. After finding out the value of x, we will substitute it in one of the equations to find out the value of y.

Complete step-by-step answer:
Name the equations mentioned in the question as equation 1 and equation 2, we get-
$ \Rightarrow \sqrt 2 x - \sqrt 3 y = 0$ (equation 1)
$ \Rightarrow \sqrt 3 x - \sqrt 8 y = 0$ (equation 2)
We will find out the value of x in terms of y by using one of the equations.
Let’s consider equation 1-
$
   \Rightarrow \sqrt 2 x - \sqrt 3 y = 0 \\
    \\
   \Rightarrow \sqrt 2 x = \sqrt 3 y \\
    \\
   \Rightarrow x = \dfrac{{\sqrt 3 }}{{\sqrt 2 }}y \\
$
Now, using the method of substitution, we will put this value of x mentioned above into equation 2 to find out the value y-
$
   \Rightarrow \sqrt 3 x - \sqrt 8 y = 0 \\
    \\
   \Rightarrow \sqrt 3 .\dfrac{{\sqrt 3 }}{{\sqrt 2 }}y - \sqrt 8 y = 0 \\
    \\
   \Rightarrow \dfrac{3}{{\sqrt 2 }}y - \sqrt 8 y = 0 \\
    \\
   \Rightarrow \left( {\dfrac{3}{{\sqrt 2 }} - \sqrt 8 } \right)y = 0 \\
    \\
   \Rightarrow y = 0 \\
$
Now, we already knew that $x = \dfrac{{\sqrt 3 }}{{\sqrt 2 }}y$. We will put the value of y we found above into this value of x; we get-
$
   \Rightarrow x = \dfrac{{\sqrt 3 }}{{\sqrt 2 }}y \\
    \\
   \Rightarrow x = \dfrac{{\sqrt 3 }}{{\sqrt 2 }}.0 \\
    \\
   \Rightarrow x = 0 \\
$
Thus, the value of x and y is $x = 0,y = 0$.

Note: Such questions are very easy to solve once you use the method of elimination by equation the coefficients or the method of substitution. We have used the method of substitution in the solution above. Remember to find out the value of x in the end because the value found before was in terms of y.