Chapter 6.2, Problem 22PPE

To determine

To solve: The system of linear equations using substitution.

Answer to Problem 22PPE

x = 1 and y = 3

Explanation of Solution

Given information:

The equations $4y-x=5+2y$ and $3x+7y=24$

Calculation:

Simplify equation $4y-x=5+2y$ to obtain value of x in form of y .

  $\begin{array}{l}4y-x=5+2y\\ \Rightarrow -x=5+2y-4y\\ \Rightarrow -x=5-2y\\ \Rightarrow x=2y-5\end{array}$

Substitute $2y-5$ for x in equation $3x+7y=24$

  $3\left(2y-5\right)+7y=24$

Now simplify above equation.

  $\begin{array}{l}3\left(2y-5\right)+7y=24\\ \Rightarrow 6y-15+7y=24\\ \Rightarrow 13y=24+15\\ \Rightarrow 13y=39\\ \Rightarrow y=3\end{array}$

Use above value ofy in equation $x=2y-5$

  $\begin{array}{c}x=2\left(3\right)-5\\ =6-5\\ =1\end{array}$

Therefore the solution is x = 1 and y = 3.

Check

  $\begin{array}{l}4y-x=5+2y3x+7y=24\\ 4\left(3\right)-1=5+2\left(3\right)3\left(1\right)+7\left(3\right)=24\\ 12-1=5+63+21=24\\ 11=1124=24\end{array}$