Chapter 9, Problem 38CR

To determine

To solve the system of equations algebraically.

Answer to Problem 38CR

The solution of the system of equations is $\left(-3,-6\right)$ .

Explanation of Solution

Given information:

The given equations are:

  $\begin{array}{l}-4\text{x}+\text{y}=6\\ -5\text{x}-\text{y}=21\end{array}$

Calculation :

Solve the first equation for $\text{y}$ :

  $\begin{array}{l}-4\text{x}+\text{y}=6\\ \text{y}=4\text{x}+6\left[\text{Add both sides by 4x}\right]\end{array}$

Substitute $\text{y}$ in second equation:

  $\begin{array}{l}-5\text{x}-\text{y}=21\\ -5\text{x}-\left(4\text{x}+6\right)=21\\ -5\text{x}-\text{4x}-6=21\\ -9\text{x}=21+6\\ -9\text{x}=27\\ \text{x}=\frac{27}{-9}\\ \text{x}=-3\end{array}$

Find $\text{y}$ , by substituting the value of $\text{x}$ :

  $\begin{array}{l}\text{y}=4\text{x}+6\\ \text{y}=4\left(-3\right)+6\\ \text{y}=-12+6\\ \text{y}=-6\end{array}$

Hence, the solution of the system of equations is $\left(-3,-6\right)$ .