Chapter 9.4, Problem 21WE

To determine

To find: The value of $x$ and $y$ by solving the given two linear equation.

Answer to Problem 21WE

The value of $x$ is $2$ and the value of $y$ is $0$ .

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{c}4\left(x-2y\right)=8\dots \left(1\right)\\ x+6y=2\dots \left(2\right)\end{array}$

To solve the given equations by substitution method, first, express the equation $\left(2\right)$ , as $x$ in terms of $y$ and then substitute the value of $x$ in equation $\left(1\right)$ So, the equation $\left(2\right)$ as $x$ in terms of $y$ is given as:

  $x=2-6y\dots \left(3\right)$

After substituting the above value of $x$ in equation $\left(1\right)$ , the calculation is as given:

  $\begin{array}{c}4\left(\left(2-6y\right)-2y\right)=8\\ \left(2-8y\right)=2\\ 8y=0\\ y=0\end{array}$

Further simplified, after substituting the value of $y=0$ in the equation $\left(3\right)$ , is as:

  $\begin{array}{c}x=2-6\left(0\right)\\ =2\end{array}$

Therefore, the value of $x$ is $2$ and the value of $y$ is $0$ .