Chapter 6.4, Problem 11P

Solve each system. Explain why you chose the method you used.

$3x-2y=8$

$2x-2y=5$

To determine

To solve the given system of equations.

Answer to Problem 11P

  $x=3,y=\frac{1}{2}$

Explanation of Solution

Given:

  $\begin{array}{l}3x-2y=8\\ 2x-2y=5\end{array}$

Calculation:

  $\begin{array}{l}3x-2y=8\to \left(1\right)\\ 2x-2y=5\to \left(2\right)\end{array}$

We choose elimination method to solve this system of equations, because the coefficient of y in both the equations is same & so we can eliminate y easily to get the value of x.

Now subtracting equation (2) from equation (1), we get

  $\begin{array}{l}\left(3x-2y\right)-\left(2x-2y\right)=8-5\\ \Rightarrow x=3\end{array}$

Now put $x=3$ in equation (1), we get

  $\begin{array}{l}3\left(3\right)-2y=8\\ \Rightarrow 2y=1\\ \Rightarrow y=\frac{1}{2}\end{array}$

Therefore the solution is,

  $x=3,y=\frac{1}{2}$