Chapter 5.1, Problem 24E

To determine

To find: The solution of linear equation using the graphical calculator.

Answer to Problem 24E

  $\left(x,y\right)=\left(5,5\right)$

Explanation of Solution

Given information:

The system of linear equation as given below,

  $\begin{array}{l}-1.6x-3.2y=-24\\ 2.6x+2.6y=26\end{array}$

Formula used:

Substitution method is used.

Calculation:

The equation $2.6x+2.6y=26$ for $x$

Move the variable $2.6y$ to the right side and change its sign

  $2.6x=26-2.6y$

Divide both sides by (2.6)

  $x=\left(26-2.6y\right)\times \frac{5}{13}$

Convert the decimal number into a fraction

  $x=\left(26-\frac{13}{5}y\right)\times \frac{5}{13}$

Distribute $\frac{5}{13}$ through the parenthesis

  $x=10-y$

Substitute the value of x into the equation

  $\begin{array}{l}-1.6x-3.2y=-24\\ -1.6\left(10-y\right)-3.2y=-24\end{array}$

Solve the equation for y

  $y=5$

Substitute the value of y into the equation $x=10-y$

  $\begin{array}{l}x=10-5\\ x=5\end{array}$

The possible solution of the system is the ordered pair $\left(x,y\right)=\left(5,5\right)$

Check if the ordered pair is the solution of the system of equations

  $\begin{array}{l}-1.6\times 5-3.2\times 5=-24\\ 2.6\times 5+2.6\times 5=26\end{array}$

Simplify the equalities

  $\begin{array}{l}-24=-24\\ 26=26\end{array}$

Since all of the equalities are true, the ordered pair (5, 5) is the solution of the system

  

Conclusion:

The value is $\left(x,y\right)=\left(5,5\right)$