Question

Solve the following equations by the substitution method :

$$\begin{gathered} x+2y=1.6 \\ 2x+y=14 \end{gathered}$$

Answer 1

Step 1:Express x in terms of y:

Given equations,

$$\begin{gathered} x+2y=1.6..................................................\left(1\right) \\ 2x+y=1.4..................................................\left(2\right) \end{gathered}$$

Consider the first equation,

$$\begin{gathered} x+2y=1.6 \\ \Rightarrow x=1.6-2y..........................................\left(3\right) \end{gathered}$$

Step2: Substitute this value of x obtained from equation (3) in equation(2):

Substituting the x value in $2x+y=1.4$,we get

$$\begin{gathered} 2(1.6-2y)+y=1.4 \\ \Rightarrow 3.2-4y+y=1.4 \\ \Rightarrow 3.2-3y=1.4 \\ \Rightarrow 3.2-1.4=3y \\ \Rightarrow 1.8=3y \\ \Rightarrow y=\frac{1.8}{3} \\ \Rightarrow y=0.6 \end{gathered}$$

Step (3) : Substitute the values of y obtained from equation (2) in equation (3):

$$\begin{gathered} x=1.6-2y \\ =1.6-(2\times 0.6) \\ =1.6-1.2 \\ =0.4 \end{gathered}$$

Hence, the values of $x=0.4andy=0.6$.