Chapter 7.1, Problem 2E

Solution

To determine: Whether the ordered pair is a solution of the system.

a. $\left(2,-3\right)$ and c. $\left(6,5\right)$ are the solution of the given system.

Given: System of equations:

  $\begin{array}{l}y=x^2-6x+5\mathrm{...}\text{(}i\text{)}\\ y=2x-7\mathrm{...}\text{(}ii\text{)}\end{array}$

Ordered pairs:

  $\begin{array}{l}a.\left(2,-3\right)\\ b.\left(1,-5\right)\\ c.\left(6,5\right)\end{array}$

Calculation:

a. Substitute $x=2$ and $y=-3$ in $\left(i\right)$

  $\begin{array}{l}-3={\left(2\right)}^2-6\left(2\right)+5\\ -3=4-12+5\\ -3=-3\end{array}$

which is true.

Substitute $x=2$ and $y=-3$ in $\left(ii\right)$

  $\begin{array}{l}-3=2\left(2\right)-7\\ -3=4-7\\ -3=-3\end{array}$

which is true.

Hence, $\left(2,-3\right)$ is a solution of the given system.

b. Substitute $x=1$ and $y=-5$ in $\left(i\right)$

  $\begin{array}{l}-5={\left(1\right)}^2-6\left(1\right)+5\\ -5=1-6+5\\ -5=0\end{array}$

which is not true.

  $\left(1,-5\right)$ is not a solution of the given system.

c. Substitute $x=6$ and $y=5$ in $\left(i\right)$

  $\begin{array}{l}5={\left(6\right)}^2-6\left(6\right)+5\\ 5=36-36+5\\ 5=5\end{array}$

which is true.

Substitute $x=6$ and $y=5$ in $\left(ii\right)$

  $\begin{array}{l}5=2\left(6\right)-7\\ 5=12-7\\ 5=5\end{array}$

which is true.

Hence, $\left(6,5\right)$ is a solution of the given system.

Conclusion:

a. $\left(2,-3\right)$ and c. $\left(6,5\right)$ are the solution of the given system.