Chapter 5.1, Problem 24E

To determine

To solve: the system linear equation.

Answer to Problem 24E

The ordered pair is(5,5)

Explanation of Solution

Given:

  $-1.6x-3.2y=-24$

  $2.6x+2.6y=26$

Calculation:

Solve the equation $2.6x+2.6y=26$ for $x$

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

  $2.6x=26-2.6y$

Divide both sides by (2.6)

  $x=(26-2.6y)\times \frac{5}{13}$

Convert the decimal number into a fraction

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

Distribute $\left(\frac{5}{13}\right)$ through the parenthesis

  $x=10-y$

Substitute the value of $x$ into the equation $-1.6x-3.2y=-24$

  $-1.6(10-y)-3.2y=-24$

Solve the equation for $y$

  $y=5$

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

  $x=10-5$

  $x=5$

The ordered pair $(x,y)=(5,5)$

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

  $-1.6\times 5-3.2\times 5=-24$

  $2.6\times 5+2.6\times 5=26$

Simplify the equalities

  $-24=-24$

  $26=26$

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

  

Conclusion:

The ordered pair is(5,5)