Chapter 8.10, Problem 26HP

To determine

The solution of the $x+4y=33$ and $y=-3x$ by using the substitution method

Answer to Problem 26HP

The solution of $x+4y=33$ and $y=-3x$ is $x=-3$ and $y=9$ .

Explanation of Solution

Given:

The two eqn are as:

  $\begin{array}{l}x+4y=33\\ y=-3x\end{array}$

Calculation:

The two eqns. are described as:

  $x+4y=33$  .... (1)

  $y=-3x$  .... (2)

Put the value of the $y=-3x$ in eq. (1):

  $\begin{array}{l}x+4y=33\\ x+4\left(-3x\right)=33\\ x-12x=33\\ -11x=33\\ x=-3\end{array}$

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

  $\begin{array}{l}y=-3x\\ y=-3\left(-3\right)\\ y=9\end{array}$

Conclusion:

Hence, the solution of the eqns. is $x=-3$ and $y=9$ .