Chapter 8, Problem 1MCCP

In Exercises 1-12, solve each system by the method of your choice.

$\{\begin{array}{l}x=3y-7\\ 4x+3y=2\end{array}$

To determine

To calculate: The solution of system of equations $x=3y-7,4x+3y=2$.

Answer to Problem 1MCCP

Solution: The solution is $\underset{\_}{\left(-1,2\right)}$.

Explanation of Solution

Given: The system of equation is,

$\begin{array}{ccc}\hfill x& =& 3y-7\hfill \\ \hfill 4x+3y& =& 2\hfill \end{array}$

Formula used: Substitution method.

Calculation:

The system of equation is,

$\begin{array}{ccc}\hfill x& =& 3y-7\left(1\right)\hfill \\ \hfill 4x+3y& =& 2\left(2\right)\hfill \end{array}$

Put the value of $x$ from equation (1) in equation (2) so that:

$\begin{array}{ccc}\hfill 4\left(3y-7\right)+3y& =& 2\hfill \\ \hfill 12y-28+3y& =& 2\hfill \\ \hfill 15y& =& 30\hfill \\ \hfill y& =& 2\hfill \end{array}$

Now put $y=2$ in equation (1):

$\begin{array}{l}x=3\left(2\right)-7\\ x=-1\end{array}$

The solution is $\left(-1,2\right)$.