Chapter 11, Problem 98RE

To determine

Find $A$ so that the system of equations is inconsistent.

Answer to Problem 98RE

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

Explanation of Solution

Given information:

Find $A$ so that the system of equations is inconsistent.

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

Calculation:

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

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

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

The value of determinant is zero for all values of $A$ .

Hence the system of equations is inconsistent for all the values of $A$ .