Chapter 2, Problem 1RE

To determine

Whether the ordered pairs $\left(-2,3\right),\left(0,-5\right),\left(2,-3\right)\left(3,-2\right),\left(4,3\right)\text{ and }\left(7,2\right)$ are the solution of the equation $y=x^2-2x-5$.

Answer to Problem 1RE

Solution:

The ordered pairs $\underset{\_}{\left(-2,3\right)\left(0,-5\right),\left(3,-2\right),\left(4,3\right)}$ are solution of the equation $y=x^2-2x-5$.

Explanation of Solution

Given:

The expression is $y=x^2-2x-5$.

Explanation:

For $\left(-2,3\right)$ be the solution of the provided equation, put $x=-2\text{ and }y=3$. So,

$\begin{array}{ccc}\hfill 3& =& {\left(-2\right)}^2-2\left(-2\right)-5\hfill \\ \hfill & =& 4+4-5\hfill \\ \hfill & =& 3\hfill \end{array}$

So, left hand side is equal to right hand side.

Therefore, $\left(-2,3\right)$ is solution of the provided expression.

Now, for $\left(0,-5\right)$ be the solution of the provided equation, put $x=0\text{ and }y=-5$. So,

$\begin{array}{ccc}\hfill -5& =& {\left(0\right)}^2-2\left(0\right)-5\hfill \\ \hfill & =& 0-0-5\hfill \\ \hfill & =& -5\hfill \end{array}$

So, left hand side is equal to right hand side.

Therefore, $\left(0,-5\right)$ is solution of the provided expression.

Now, for $\left(2,-3\right)$ be the solution of the provided equation put $x=2\text{ and }y=-3$. So,

$\begin{array}{ccc}\hfill -3& =& {\left(2\right)}^2-2\left(2\right)-5\hfill \\ \hfill & =& 4-4-5\hfill \\ \hfill & =& -5\hfill \end{array}$

So, left hand side is not equal to right hand side.

Therefore, $\left(2,-3\right)$ is not the solution of the provided expression.

Now, for $\left(3,-2\right)$ be the solution of the provided equation, put $x=3\text{ and }y=-2$. So,

$\begin{array}{ccc}\hfill -2& =& {\left(3\right)}^2-2\left(3\right)-5\hfill \\ \hfill & =& 9-6-5\hfill \\ \hfill & =& -2\hfill \end{array}$

So, left hand side is equal to right hand side.

Therefore, $\left(3,-2\right)$ is the solution of the provided expression.

For $\left(4,3\right)$ be the solution of the provided equation, put $x=4\text{ and }y=3$. So,

$\begin{array}{ccc}\hfill 3& =& {\left(4\right)}^2-2\left(4\right)-5\hfill \\ \hfill & =& 16-8-5\hfill \\ \hfill & =& 3\hfill \end{array}$

So, left hand side is equal to right hand side.

Therefore, $\left(4,3\right)$ is solution of the provided expression.

Now, for $\left(7,2\right)$ be the solution of the provided equation put $x=2\text{ and }y=-3$. So,

$\begin{array}{ccc}\hfill 2& =& {\left(7\right)}^2-2\left(7\right)-5\hfill \\ \hfill & =& 49-14-5\hfill \\ \hfill & =& 30\hfill \end{array}$

So, left hand side is not equal to right hand side.

Therefore, $\left(7,2\right)$ is not the solution of the provided expression.