Question

Create a third equation that could be added to the system so that this solution does not change the graph line on the coordinate plane above (PART C)

Answer 1

Given that the solution of the initial system of equations is (1,4), we need to find a third line such that it goes through (1,4); then,

$\begin{gathered} y=ax+b \\ and \\ (1,4) \\ \Rightarrow4=a+b \end{gathered}$

We can set any value for a; for example, a=1; thus,

$\begin{gathered} a=1 \\ \Rightarrow4=1+b \\ \Rightarrow b=3 \end{gathered}$

Therefore, one possible third line is

$y=x+3$

The green line is the one you need to graph, the others have already been plotted.