Question

Find the value of x and y rom the following equation
\[\begin{array}{l}
0.2x + 0.1y = 25\\
2(x - 2) - 1.6y = 116
\end{array}\]

Answer 1

Hint: It is a question of linear equations in 2 variables and we are told to find the value of those variables, so we can use the 2 equations given to us and apply either substitution or elimination method to make the question look easy and find the value of x and y.

Complete step by step answer:
So the two equations given to us are
\[\begin{array}{l}
0.2x + 0.1y = 25..................................(i)\\
2(x - 2) - 1.6y = 116..............................(ii)
\end{array}\]
Now I will use the elimination method to solve this question and for that let me solve the equation (i) a bit
\[\begin{array}{l}
\therefore 0.2x + 0.1y = 25\\
 \Rightarrow \dfrac{2}{{10}}x + \dfrac{1}{{10}}y = 25\\
 \Rightarrow 2x + y = 250
\end{array}\]
So now the modified equation (i) is \[2x + y = 250\] so let it be equation (iii)
Now equation (ii) will become
\[\begin{array}{l}
\therefore 2(x - 2) - 1.6y = 116\\
 \Rightarrow 2x - 4 - 1.6y = 116\\
 \Rightarrow 2x - 1.6y = 120
\end{array}\]
Which means that the modified version of equation (ii) is \[2x - 1.6y = 120\] let it be equation (iv)
So if we look closely the coefficients of x in equation (iii) and equation (iv) are the same, which means we can use the elimination method now.
So let us subtract equation (iv) from (iii) and we will get it as
\[\begin{array}{l}
 \Rightarrow 2x + y - \left( {2x - 1.6y} \right) = 250 - 120\\
 \Rightarrow 2x + y - 2x + 1.6y = 130\\
 \Rightarrow y + 1.6y = 130\\
 \Rightarrow 2.6y = 130\\
 \Rightarrow y = \dfrac{{130}}{{2.6}}\\
 \Rightarrow y = \dfrac{{1300}}{{26}}\\
 \Rightarrow y = \dfrac{{100}}{2}\\
 \Rightarrow y = 50
\end{array}\]
So now as we have the value of y let us put it in equation (iii) to get the value of x.
\[\begin{array}{l}
 \Rightarrow 2x + y = 250\\
 \Rightarrow 2x + 50 = 250\\
 \Rightarrow 2x = 250 - 50\\
 \Rightarrow 2x = 200\\
 \Rightarrow x = \dfrac{{200}}{2}\\
 \Rightarrow x = 100
\end{array}\]

So now it is clear that the value of x is 100 and y is 50

Note: We could have also used the substitution method to solve this question, ion that we have to take out the value of either x or y manipulating either one of the equation from (i) or (ii) then we will put the value of that variable in the other equation then we will get the value of the unsubstituted variable and from there we can get the value of the substituted variable by the same process mentioned in the elaborative answer.