Chapter 9.7, Problem 10IP

To determine

To solve : the given system of equations.

Answer to Problem 10IP

The solution of the given system of equations is $\text{(}4,5)$ .

Explanation of Solution

Given information :

The given system of equations:

  $\begin{array}{l}7x-5y=3\\ x=4\end{array}$

Calculation :

As per problem,

Consider the system of equations:

  $\begin{array}{l}7x-5y=3\\ x=4\end{array}$

Since $x=4$ , replace $x$ with $4$ in the first equation.

  $\begin{array}{l}7x-5y=3\text{ [Write the first equation]}\\ 7(4)-5y=3\text{ [Replace }x\text{ with 4]}\\ 28-5y=3\text{ [Simplify]}\\ 28-5y-28=3-28\text{ [Subtract 28 from each side]}\\ -5y=-25\text{ [Simplify]}\\ \frac{-5y}{-5}=\frac{-25}{-5}\text{ [Divide both sides by }-\text{5]}\\ y=5\text{ [Simplify]}\end{array}$

The solution of this system of equations is $\text{(}4,5)$ .