Chapter 11, Problem 7RE

To determine

To find: The solution equation is $\left\{\begin{array}{l}2x+5y=10\\ 4x+10y=20\end{array}\right\}$

Answer to Problem 7RE

The solution are $x=\frac{10-5y}{2}$ and $y=\frac{10-2y}{5}$

Explanation of Solution

Given information:

The given equation is $\left\{\begin{array}{l}2x+5y=10\\ 4x+10y=20\end{array}\right\}$ .

Calculation:

Calculate the equation,

  $\left\{\begin{array}{l}2x+5y=10\\ 4x+10y=20\end{array}\right\}$

The first equation be multiply by 2 and second equation can be multiply by 1.

  $\begin{array}{l}\left\{\begin{array}{l}(2x+5y=10)\times 2\\ (4x+10y=20)\times 1\end{array}\right\}\\ \left\{\begin{array}{l}4x+10y=20\\ 4x+10y=20\end{array}\right\}\end{array}$

The equation is obtained by multiplying are same. The solution will be infinite in number of solution will be given by the either of the expressions.

  $x=\frac{10-5y}{2}$

  $y=\frac{10-2y}{5}$