Answer:
[tex] \rm x=\frac{46}{3} [/tex]
[tex] \rm y=-\frac{25}{24} [/tex]
Step-by-step explanation:
[tex] \huge\begin{array} {|c|} \hline\left. \begin{cases} { \rm\frac{ 1 }{ 4 } x+ \frac{ 4 }{ 5 } y = 3 } \\ { \rm\frac{ 5 }{ 16 } x- \frac{ 1 }{ 5 } y=5 } \end{cases} \right. \\ \hline \end{array}[/tex]
[tex] \\ \Large \overline{ \rm - \: Steps \: using \: substitution \: - }[/tex]
[tex] \rm \frac{1}{4}x+\frac{4}{5}y=3 [/tex]
[tex] \rm \frac{1}{4}x=-\frac{4}{5}y+3 [/tex]
[tex] \rm x=4\left(-\frac{4}{5}y+3\right) [/tex]
[tex] \rm x=-\frac{16}{5}y+12 [/tex]
┈
[tex] \rm \frac{5}{16}\left(-\frac{16}{5}y+12\right)-\frac{1}{5}y=5 [/tex]
[tex] \rm -y+\frac{15}{4}-\frac{1}{5}y=5 [/tex]
[tex] \rm -\frac{6}{5}y+\frac{15}{4}=5 [/tex]
[tex] \rm -\frac{6}{5}y=\frac{5}{4} [/tex]
[tex] \bold{ y=-\frac{25}{24}} [/tex]
┈
[tex] \rm x=-\frac{16}{5}\left(-\frac{25}{24}\right)+12 [/tex]
[tex] \rm x=\frac{10}{3}+12 [/tex]
[tex] \bold{ x=\frac{46}{3}} [/tex]
