Chapter 6, Problem 12CR

To determine

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

Answer to Problem 12CR

Solution is $x=4\&y=7$ & the given system of equations has one solution.

Explanation of Solution

Given:

  $\begin{array}{l}y=2x-1\\ 2x+2y=22\end{array}$

Calculation:

  $\begin{array}{l}y=2x-1\to \left(1\right)\\ 2x+2y=22\to \left(2\right)\end{array}$

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

  $\begin{array}{l}2x+2\left(2x-1\right)=22\\ \Rightarrow 2x+4x-2=22\\ \Rightarrow 6x=24\\ \Rightarrow x=4\end{array}$

Now put $x=4$ in equation (1), we get

  $\begin{array}{l}y=2\left(4\right)-1\\ \Rightarrow y=8-1\\ \Rightarrow y=7\end{array}$

Therefore the solution is $x=4\&y=7$ .

Hence the given system of equations has one solution.