Question

Solve the following systems of equations:
$
  \dfrac{x}{2} + y = 0.8 \\
  \dfrac{7}{{x + \dfrac{y}{2}}} = 10 \\
$

Answer 1

Hint – We can write the first equation, $\dfrac{x}{2} + y = 0.8$ as $\dfrac{x}{2} = 0.8 - y$ and then substitute this value of x/2 in second equation to solve for x and y.

Complete step-by-step answer:
We have the equations-
$
  \dfrac{x}{2} + y = 0.8 - (1) \\
  \dfrac{7}{{x + \dfrac{y}{2}}} = 10 - (2) \\
 $
Now using the equation (1)-
$\dfrac{x}{2} + y = 0.8$
We can write-
$
  \dfrac{x}{2} = 0.8 - y \\
  x = 2(0.8 - y) \\
$
Now substituting the value of x in equation (2), we get-
$
  \dfrac{7}{{x + \dfrac{y}{2}}} = 10 \\
   \Rightarrow \dfrac{7}{{2(0.8 - y) + \dfrac{y}{2}}} = 10 \\
$
Cross multiplying the terms, we get-
$
   \Rightarrow 7 = 10\left( {2(0.8 - y) + \dfrac{y}{2}} \right) \\
   \Rightarrow 7 = 10\left( {1.6 - 2y + \dfrac{y}{2}} \right) \\
   \Rightarrow 7 = 10\left( {1.6 - \dfrac{{3y}}{2}} \right) \\
   \Rightarrow 7 = 16 - 15y \\
   \Rightarrow - 9 = - 15y \\
   \Rightarrow y = \dfrac{9}{{15}} = \dfrac{3}{5} = 0.6 \\
$
Now putting the value of y in equation (1) we get-
$
  \dfrac{x}{2} + 0.6 = 0.8 \\
  \dfrac{x}{2} = 0.8 - 0.6 \\
  x = 2 \times 0.2 = 0.4 \\
 $
Therefore, the values of x and y are 0.4 and 0.6 respectively.

Note - Whenever such types of questions appear then always write the equations given in the question then by adding and subtracting try to find the value of x or y and then by using the value of either x or y, find the other unknown variable. The method used in this question is the “substitution method”, in this method of solving, we choose any one equation from the given equations and then we substitute the value of one variable into another equation to find the other variable value, as mentioned in the solution, we have found the value of variable x terms of y and then substitute it in second equation given.