Chapter 11, Problem 53RE

To determine

To find: The value of A.

Answer to Problem 53RE

The value of A is $10$ .

Explanation of Solution

Given information:

The system of the equations is

  $\{\begin{array}{c}2x+5y=5\\ 4x+10y=A\end{array}$

Calculation:

Consider the system of the equations as

  $\{\begin{array}{c}2x+5y=5\\ 4x+10y=A\end{array}$

Solve the first equation in the system for $y$ .

  $\begin{array}{c}2x+5y=5\\ 2x+5y-2x=5-2x\\ 5y=5-2x\\ y=\frac{5-2x}{5}\end{array}$

Substitute the value in the second equation of the system.

  $\begin{array}{c}4x+10\left(\frac{5-2x}{5}\right)=A\\ 4x+10-4x=A\\ A=10\end{array}$

Therefore, the value of A is $10$ .