Chapter 8.8, Problem 38E

To determine

Which ordered pair is nota solution of the linear system $y=2x+16\text{ and }y=-x+1$ ?

Answer to Problem 38E

The ordered pair $(-5,6)$ is a solution for the given system and option C is the correct choice.

Explanation of Solution

Given:

Four choices:

  $\text{A}\text{. (}0,16)\text{ B}\text{. (2,}-\text{1) C}\text{. (}-5,6)\text{ D}\text{. (}-8,9)$

Calculation:

We have been given a system of equations. We will solve our system using substitution method.

Upon equating both equations, we will get:

  $2x+16=-x+1$

Let us solve for x.

  $\begin{array}{l}2x+16=-x+1\\ 2x+x+16=-x+x+1(\text{Adding }x\text{ on both sides)}\\ 3x+16=1\\ 3x+16-16=1-16(\text{Subtracting 16 from both sides)}\\ 3x=-15\\ \frac{3x}{3}=-\frac{15}{3}(\text{Dividing both sides by }3)\\ x=-5\end{array}$

Now, we will substitute $x=-5$ in equation $y=-x+1$ to solve for y.

  $\begin{array}{l}y=-x+1\\ y=-(-5)+1\left(\text{Substituting }x=-5\right)\\ y=5+1\\ y=6\end{array}$

Therefore, the ordered pair $(-5,6)$ is a solution for the given system and option C is the correct choice.