Chapter 6.1, Problem 54PFA

To determine

Find system of equation could have $(1,5)$ as a solution if $b<0\&c>0$ .

Answer to Problem 54PFA

The system of equation is, C. $\begin{array}{l}y=2x+3\\ y=bx+c\end{array}$

Explanation of Solution

Given information:

It is given in the question that,

A. $\begin{array}{l}y=-x+6\\ y=-x+b\end{array}$

B. $\begin{array}{l}y=-x+6\\ y=cx+6\end{array}$

C. $\begin{array}{l}y=2x+3\\ y=bx+c\end{array}$

D. $\begin{array}{l}y=2x+3\\ y=2x+b\end{array}$

Only,

C. $\begin{array}{l}y=2x+3\\ y=bx+c\end{array}$

By putting the value $(1,5)$ only the above equation,

  $y=2x+3\Rightarrow 5=2+3\Rightarrow 5=5$

  $y=2x+b\Rightarrow 5=b+c$

Then some cases arise where $y=2x+b\Rightarrow 5=b+c$ may satisfied when $b<0\&c>0$