\documentclass[10pt]{article}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}

\begin{tikzpicture}[x=1cm,y=1cm]
\begin{axis}[
x=1cm,y=1cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-3.5301370701590713,
xmax=7.701311755516924,
ymin=-0.5,
ymax=4.5,
xtick={-3,...,7},
ytick={-3,-2,...,6},]
\clip(-3.5301370701590713,-3.410207869386736) rectangle (7.701311755516924,6.144461052102637);
\draw [-latex,line width=1pt] (0,0) -- (7,2);
\draw [-latex,line width=1pt] (0,0) -- (-3,2);
\draw [-latex,line width=2pt,color=blue] (0,0) -- (4,4);
\draw [-latex,line width=1pt,color=red,dashed] (-3,2) -- (4,4);
\draw [-latex,line width=1pt,color=red,dashed] (7,2) -- (4,4);
\begin{scriptsize}


\draw[color=blue] (3.5242446569218764,1.3) node {$\overrightarrow{y}$};
\draw[] (-2.2,1.08) node {$\overrightarrow{x}$};
\draw[color=blue] (1.4,2.151) node {$\overrightarrow{x+y}$};
\draw[color=red] (0.5278687334641462,3.3) node {$\overrightarrow{y'}$};
\draw[color=red] (5.2,2.8) node {$\overrightarrow{x}'$};
\end{scriptsize}
\end{axis}
\end{tikzpicture}
\end{document}