Chapter 8.10, Problem 27HP

To determine

The solution of the $5x+y=8$ and $y=x-4$ by using the substitution method

Answer to Problem 27HP

The solution of $5x+y=8$ and $y=x-4$ is $x=2$ and $y=-2$ by using the substitution method.

Explanation of Solution

Given:

The two eqn are as:

  $5x+y=8$ and $y=x-4$

Calculation:

The two eqns. are described as:

  $5x+y=8$....... (1)

  $y=x-4$....... (2)

Put the value of the $y=x-4$ in eq. (1):

  $\begin{array}{l}5x+y=8\\ 5x+x-4=8\\ 6x=12\\ x=2\end{array}$

Now, calculate the value of $y$ by using eq. (2):

  $\begin{array}{l}y=x-4\\ y=2-4\\ y=-2\end{array}$

Conclusion:

Hence, the solution of the eqns. is $x=2$ and $y=-2$ .