Question

Solve the following system of equations-
$
  0.5x + 0.7y = 0.74 \\
    \\
  0.3x + 0.5y = 0.5 \\
$

Answer 1

Hint- We will use the method of elimination by equating the coefficients in order to solve this question. After doing so, we will also use subtraction like in the solution below to find out the value of x and y.

Complete step-by-step answer:
Mark the equations given in the question as equation 1 and equation 2 respectively, we will get:
$ \Rightarrow 0.5x + 0.7y = 0.74$ (equation 1)
$ \Rightarrow 0.3x + 0.5y = 0.5$ (equation 2)
Now, in order to use the method of elimination by making the coefficients equal, we will multiply the equation 1 by 3 and equation 2 by 5 so that the coefficients of x in both the equations will be equal, we will get-
Equation 1-
$
   \Rightarrow \left( {0.5x + 0.7y = 0.74} \right) \times 3 \\
    \\
   \Rightarrow 1.5x + 2.1y = 2.22 \\
$
Marking the above equation as equation 3-
$ \Rightarrow 1.5x + 2.5y = 2.5$ (equation 3)
Equation 2-
$
   \Rightarrow \left( {0.3x + 0.5y = 0.5} \right) \times 5 \\
    \\
   \Rightarrow 1.5x + 2.5y = 2.5 \\
$
Marking the above equation as equation 4-
$ \Rightarrow 1.5x + 2.5y = 2.5$ (equation 4)
Subtracting equation 3 from equation 4, we get-
$
   \Rightarrow 1.5x + 2.5y - 1.5x - 2.1y = 2.5 - 2.22 \\
    \\
   \Rightarrow 0.4y = 0.28 \\
    \\
   \Rightarrow y = 0.7 \\
$
Now, we will put the value of y into equation 2 in order to get the value of x-
$
   \Rightarrow 0.3x + 0.5\left( {0.7} \right) = 0.5 \\
    \\
   \Rightarrow 0.3x = 0.5 - 0.35 \\
    \\
   \Rightarrow 0.3x = 0.15 \\
    \\
   \Rightarrow x = 0.5 \\
$
Thus, the value of x and y is $x = 0.5,y = 0.7$.

Note: Such questions are very easy to solve once we use the method of elimination by equating the coefficients and the method of substitution. Remember to equate the coefficients if we use the method of elimination.