Write the matrix equation for this system and use it to solve the system.

{4x+2y+4z+4w=2216x+7y+4z+16w=498x4y2z8w=268x4y8z6w=46\displaystyle {\left\lbrace\begin{array}{ccccccccc} -{4}{x}&+&{2}{y}&+&{4}{z}&+&{4}{w}&=&-{22}\\-{16}{x}&+&{7}{y}&+&{4}{z}&+&{16}{w}&=&-{49}\\{8}{x}&-&{4}{y}&-&{2}{z}&-&{8}{w}&=&{26}\\{8}{x}&-&{4}{y}&-&{8}{z}&-&{6}{w}&=&{46}\end{array}\right.}

x =  
y =  
z =  
w =