Chapter 11, Problem 54RE

To determine

To find: The value of A at which the system of equations is inconsistent.

Answer to Problem 54RE

The system of the equation is inconsistent for all the values of the $A$ .

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

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

The system of equation is inconsistent if the value of the determinant formed by the coefficients of the variables in the equation is zero. The determinant from the equation can be obtained and the determined as follows.

  $\begin{array}{c}\left|\begin{array}{cc}2& 5\\ 4& 10\end{array}\right|=\left(2\times 10\right)-\left(5\times 4\right)\\ =20-20\\ =0\end{array}$

The value of the determinant of the coefficient of the variables in the given system of equations is zero for all values of $A$ . Hence, the system of the equation is inconsistent for all the values of the $A$ .

Therefore, the system of the equation is inconsistent for all the values of the $A$ .