Q. 54 - Precalculus Enhanced with Graphing Utilities

Question

Find A so that the system in Problem 53 is inconsistent.

Step-by-Step Solution

Answer

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

Step 1. Given

The system of equations:

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

Step 2. Inconsistent system

The system of equation is inconsistent if the determinant formed by the coefficients of the variables is zero.

Step 3. Find the determinant value.

Determinant of coefficient of variables is:

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

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