Chapter SH, Problem 6.5.6EP

To determine

The best method to solve the system of equations and their solution.

Answer to Problem 6.5.6EP

Elimination method.

The solution is $x=\frac{19}{4},y=-14$ .

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{l}4x+y=5\\ -4x-2y=9\end{array}$

Calculation:

The best method to solve the system is elimination.

The solution will be:

  $\begin{array}{l}4x+y=5\\ \underset{\_}{-4x-2y=9}\\ \text{ - y = 14}\\ \text{ y = -14}\end{array}$

Put $\text{ y = -14}$ in $4x+y=5$ :

  $\begin{array}{l}4x+y=5\\ 4x+\left(-14\right)=5\\ 4x=5+14\\ 4x=19\\ x=\frac{19}{4}\end{array}$

The solution is $x=\frac{19}{4},y=-14$ .