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Coldprinceidn

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]

Mhanifaidn

Answer:

  • (46/3, - 25/24)

Step-by-step explanation:

It is easier to solve it by elimination.

Add the first equation to 4 times the second one to eliminate y:

  • 1/4x + 4/5y + 4*5/16x - 4/5y = 3 + 4*5
  • 1/4x + 5/4x = 3 + 20
  • 6/4x = 23
  • 3/2x = 23
  • x = 2*23/3
  • x = 46/3

Now find y:

  • 1/4*46/3 + 4/5y = 3
  • 23/6 + 4/5y = 3
  • 4/5y = 3 - 23/6
  • 4/5y = -5/6
  • y = -25/24
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