Question

Solve the following equations by the substitution method :

$$\begin{gathered} 5x+2y=14 \\ x+3y=8 \end{gathered}$$

Answer 1

Step(1):Express one variable (say x) in terms of other variable (say y) from one of the given equations.

Given equations,

$$\begin{gathered} 5x+2y=14...........................................\left(1\right) \\ x+3y=8..............................................\left(2\right) \end{gathered}$$

consider the second equation,

$$\begin{gathered} x+3y=8 \\ x=8-3y............................................\left(3\right) \end{gathered}$$

Step (2):Substitute this value of $x=8-3y$ in equation(1):

Consider the first equation,

$5x+2y=14$

Substitute the value of $x=8-3y$ in equation (1), We will get

$$\begin{gathered} 5(8-3y)+2y=14 \\ \Rightarrow 40-15y+2y=14 \\ \Rightarrow 40-13y=14 \\ \Rightarrow 40-14=13y \\ \Rightarrow 26=13y \\ \Rightarrow y=\frac{26}{13} \\ \Rightarrow y=2 \end{gathered}$$

Step (3) : Substitute the values of $y=2$ obtained from equation (1) in equation (2):

we will get the values for x

$$\begin{gathered} x=8-3y \\ \Rightarrow x=8-(3\times 2) \\ \Rightarrow x=8-6 \\ \Rightarrow x=2 \end{gathered}$$

Hence, the values of $x=2andy=2$