Given:
The system of equations is
[tex]y=x-3[/tex] ...(i)
[tex]y=-2x+1[/tex] ...(ii)
To find:
The set of coordinates that satisfies the system of equations.
Solution:
On equating the given equations, we get
[tex]x-3=-2x+1[/tex]
[tex]x+2x=3+1[/tex]
[tex]3x=4[/tex]
Divide both sides by 3.
[tex]x=\dfrac{4}{3}[/tex]
Putting [tex]x=\dfrac{4}{3}[/tex] in (i), we get
[tex]y=\dfrac{4}{3}-3[/tex]
[tex]y=\dfrac{4-9}{3}[/tex]
[tex]y=\dfrac{-5}{3}[/tex]
Therefore, the required set of coordinates that satisfies the given system of equations is [tex]\left(\dfrac{4}{3},\dfrac{-5}{3}\right)[/tex].
