Chapter 11.1, Problem 84AYU

To determine

To explain:The preferred method among substitution and elimination to solve system of two linear equations containing two variables.

Answer to Problem 84AYU

The preferred method is elimination.

Explanation of Solution

Given information:

The methods substitution and elimination.

Calculation:

To solve a system of two linear equation with two variables, the method of elimination is preferred as it much simpler and avoid any fractional term. One variable is eliminated easily when equations are transformed.

Consider the system of equations

  $\begin{array}{c}x+2y=7\\ y=5x-2\end{array}$

Multiply the second equation by 2,

  $\begin{array}{c}2y=10x-2\\ 10x-2y=4\end{array}$

Rewrite the system as,

  $\begin{array}{c}x+2y=7\\ 10x-2y=4\end{array}$

Use the method of elimination to solve the system above.

Add both the equations,

  $\begin{array}{ccccc}x& +& 2y& =& 7\\ 10x& -& 2y& =& 4\\ +& & & & \\ 11x& +& 0& =& 11\end{array}$

Therefore,

  $\begin{array}{c}11x=11\\ x=1\end{array}$

Now substitute $x=1$ in the equation $x+2y=7$ ,

  $\begin{array}{c}1+2y=7\\ 2y=6\\ y=3\end{array}$

Therefore, solution is the coordinate pair, $\left(1,3\right)$ .

Consider the system of equations

  $\begin{array}{c}x+y=6\\ 3x-2y=-2\end{array}$

Use the method of substitution to solve the system above.

From the equation $x+y=6$ isolate the value of y ,

  $\begin{array}{c}x+y=6\\ y=6-x\end{array}$

Now substitute $y=6-x$ in the equation $3x-2y=-2$ ,

  $\begin{array}{c}3x-2\left(6-x\right)=-2\\ 3x-12+2x=-2\\ 5x=-2+12\end{array}$

Simplify it further as,

  $\begin{array}{c}5x=10\\ x=2\end{array}$

Now, substitute $x=2$ in the equation $y=6-x$ ,

  $\begin{array}{c}y=6-2\\ y=4\end{array}$

Therefore, solution is the coordinate pair, $\left(2,4\right)$ .

Thus, the preferred method is elimination.