Chapter 9.7, Problem 25HP

To determine

To find : the values of $m$ and $p$ in the given system of equations.

Answer to Problem 25HP

  $m=-3$ and $p=2$ .

Explanation of Solution

Given information :

The system of equations:

  $\begin{array}{l}2x+3y=8\\ x-2y=m\end{array}$

The solution of the given system of equations is $(1,p)$ .

Calculation :

As per problem,

Consider the given system of equations:

  $\begin{array}{l}2x+3y=8\\ x-2y=m\end{array}$

The solution of this system of equations is given as $(1,p)$ .

Substitute $1$ for $x$ in the first equation to find the value of $y$ .

  $\begin{array}{l}\text{}\text{}\text{}\text{}\text{}\text{}\text{ 2}x+3y=8\text{ [Write the first equation]}\\ 2(1)+3y=8\text{ [Substitute }x=1\text{]}\\ 2+3y=8\text{ [Simplify}]\\ 2+3y-2=8-2\text{ [Subtract 2 from each side}]\\ 3y=6\text{ [Simplify}]\\ y=2\text{ [Divide both sides by 3}]\end{array}$

Therefore, $y=p=2$

Substitute $1$ for $x$ and $2$ for $y$ in the second equation to find the value of $m$ .

  $\begin{array}{l}\text{}\text{}\text{}\text{}\text{}x-2y=m\text{ [Write the second equation]}\\ 1-2(2)=m\text{ [}x=1,y=2\text{]}\\ -3=m\text{ [Simplify}]\end{array}$

Thus, $p=2$ and $m=-3$ .