Question

Solve the following equations by the substitution method :

$$\begin{gathered} x=3y-19 \\ y=3x-23 \end{gathered}$$

Answer 1

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

Given equations,

$$\begin{gathered} x=3y-19..............................................\left(1\right) \\ y=3x-23..............................................\left(2\right) \end{gathered}$$

Consider the first equation,

$x=3y-19$

Step (2): Substitute the value of $x=3y-19$ in equation (2):

$$\begin{gathered} y=3x-23 \\ \Rightarrow y=3(3y-19)-23 \\ \Rightarrow y=9y-57-23 \\ \Rightarrow y=9y-80 \\ \Rightarrow 80=9y-y \\ \Rightarrow 8y=80 \\ \Rightarrow y=\frac{80}{8} \\ \Rightarrow y=10 \end{gathered}$$

Step (3) : Substitute the values of $y=10$ obtained from equation (2) in equation(1):

we will get the values for x

$$\begin{gathered} x=3y-19 \\ \Rightarrow x=(3\times 10)-19 \\ \Rightarrow x=30-19 \\ \Rightarrow x=11 \end{gathered}$$

Hence, the values of $x=11andy=10$.