Chapter 2.1, Problem 31E

To determine

To find: which method is easier to solve the given system of equation and also find the solution.

Answer to Problem 31E

  $\begin{array}{l}a=-3\\ b=-3\end{array}$

Explanation of Solution

Given information:

The given system of equations is as follows:

  $\begin{array}{l}a-b=0\mathrm{...}\left(1\right)\\ 3a+2b=-15\mathrm{...}\left(2\right)\end{array}$

Calculation:

Substitution method is easier for solving the given system of equation because we have to just rewrite the (1) equation and then substitute it in the other equation to find the value of one variable. This method will take less time to solve the equation.

Rewrite equation (1) as follows:

  $\begin{array}{c}a-b=0\\ a=b\end{array}$

Put the value of a in equation (2) and solve it shown below.

  $\begin{array}{c}3a+2\left(a\right)=-15\\ 3a+2a=-15\\ 5a=-15\\ a=\frac{-15}{5}\\ =-3\end{array}$

Since, a and b are equal. Thus, the value for both a and b is $-3$ .