Question

Please explain how to find the answer

Answer 1

Answer:

$\rm x=\frac{46}{3}$

$\rm y=-\frac{25}{24}$

Step-by-step explanation:

$\huge\begin{array} {|c|} \hline\left. \begin{cases} { \rm\frac{ 1 }{ 4 } x+ \frac{ 4 }{ 5 } y = 3 } \\ { \rm\frac{ 5 }{ 16 } x- \frac{ 1 }{ 5 } y=5 } \end{cases} \right. \\ \hline \end{array}$

$\\ \Large \overline{ \rm - \: Steps \: using \: substitution \: - }$

$\rm \frac{1}{4}x+\frac{4}{5}y=3$

$\rm \frac{1}{4}x=-\frac{4}{5}y+3$

$\rm x=4\left(-\frac{4}{5}y+3\right)$

$\rm x=-\frac{16}{5}y+12$

┈

$\rm \frac{5}{16}\left(-\frac{16}{5}y+12\right)-\frac{1}{5}y=5$

$\rm -y+\frac{15}{4}-\frac{1}{5}y=5$

$\rm -\frac{6}{5}y+\frac{15}{4}=5$

$\rm -\frac{6}{5}y=\frac{5}{4}$

$\bold{ y=-\frac{25}{24}}$

┈

$\rm x=-\frac{16}{5}\left(-\frac{25}{24}\right)+12$

$\rm x=\frac{10}{3}+12$

$\bold{ x=\frac{46}{3}}$

Answer 2

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