Chapter 8, Problem 3CT

To determine

To tell:

Whether the ordered pairsare solution for the equation $y=7-2x$ .

Answer to Problem 3CT

The ordered pairs

  $(6,-5)$ and $(2,3)$ are solutions for the given equation.

Explanation of Solution

Given:

3 ordered pairs:

  $(5,1),(6,-5),(2,3)$

Calculation:

To check whether the ordered pair $(5,1)$ is a solution for the given equation or not, we will substitute coordinates of point $(5,1)$ in our given equation as shown below:

  $\begin{array}{l}y=7-2x\left(\text{Given equation}\right)\\ 1=7-2(5)\left(\text{Substituting }x=5\text{ and }y=1\right)\\ 1=7-10\\ 1\ne -3\end{array}$

Since both sides of equation are not equal, therefore, the ordered pair $(5,1)$ is not a solution for the given equation.

Similarly, we will check point $(6,-5)$ .

  $\begin{array}{l}y=7-2x\left(\text{Given equation}\right)\\ -5=7-2(6)\left(\text{Substituting }x=6\text{ and }y=-5\right)\\ -5=7-12\\ -5=-5\end{array}$

Since both sides of equation are equal, therefore, the ordered pair $(6,-5)$ is a solution for the given equation.

Let us check point $(2,3)$ in our given equation as shown below:

  $\begin{array}{l}y=7-2x\left(\text{Given equation}\right)\\ 3=7-2(2)\left(\text{Substituting }x=2\text{ and }y=3\right)\\ 3=7-4\\ 3=3\end{array}$

Since both sides of equation are equal, therefore, the ordered pair $(2,3)$ is a solution for the given equation.