Q. 53 - Precalculus Enhanced with Graphing Utilities

Question

Find A so that the system of equations has infinitely many
solutions.

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

Step-by-Step Solution

Answer

The system of equation has infinitely many solutions when $A=10$

Step 1. Given

The system of equations:

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

Step 2. Solve the first equation for y

Solve the first equation for y.

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

Step 3. Substitute y in second equations.

Substitute $y=\frac{5-2x}{5}$ in the second equation,

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

The system has infinitely many solution when $A=10$