Chapter 8.10, Problem 25HP

To determine

The solution of the $y=2x+6$ and $y=x$ by using the substitution method

Answer to Problem 25HP

The solution of $y=2x+6$ and $y=x$ is $x=y=-6$ .

Explanation of Solution

Given:

The two eqn are as:

  $\begin{array}{l}y=2x+6\\ y=x\end{array}$

Calculation:

The two eqns. are described as:

  $y=2x+6$....... (1)

  $y=x$....... (2)

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

  $\begin{array}{l}y=2x+6\\ x=2x+6\\ x=-6\end{array}$

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

  $\begin{array}{l}y=x\\ y=-6\end{array}$

Conclusion:

Hence, the solution of the eqns. is $x=y=-6$ .