Chapter 6, Problem 4CT

To determine

To solve the system of equations by the method of substitution.

Answer to Problem 4CT

  $x=8\&y=25$ .

Explanation of Solution

Given:

  $\begin{array}{l}y=4x-7\\ y=2x+9\end{array}$

Calculation:

  $\begin{array}{l}y=4x-7\to \left(1\right)\\ y=2x+9\to \left(2\right)\end{array}$

Now substituting equation (1) in equation (2), we get

  $\begin{array}{l}4x-7=2x+9\\ \Rightarrow 4x-2x=9+7\\ \Rightarrow 2x=16\\ \Rightarrow x=8\end{array}$

Now put $x=8$ in equation (1), we get

  $\begin{array}{l}y=4\left(8\right)-7\\ \Rightarrow y=32-7\\ \Rightarrow y=25\end{array}$

Therefore the solution is $x=8\&y=25$ .