Given:
Graph is given as
To find: Which system of equations suits the given graph.
Substitute the given point (4,-1) in the given equations one by one to find the system of equations.
By substituting the point (4,-1) in the first two options. We get,
[tex]\begin{gathered} x+y=5 \\ 4-1=5 \\ 3\ne5 \end{gathered}[/tex]
First two options doesn't suits the graph.
By Substituting in 3rd option,we get
[tex]\begin{gathered} \text{Substituting in the first equation,} \\ x-y=5 \\ 4-(-1)=5 \\ 4+1=5 \\ 5=5 \\ \text{Substituting in the second equation,} \\ x-2y=2 \\ 4-2(-1)=2 \\ 6\ne2 \end{gathered}[/tex]
By substituting in the fourth equation,
[tex]\begin{gathered} \text{Substitute in the first eqution} \\ x-y=5 \\ 4-(-1)=5 \\ 5=5 \\ \text{Substitute in the second equation} \\ x+2y=2 \\ 4+2(-1)=2 \\ 4-2=2 \\ 2=2 \end{gathered}[/tex]
Fourth option suits the given graph.
Therefore, the final answer is
[tex]x-y=5\text{ and }x+2y=2[/tex]
