Answer:
Solving the given equations we get [tex]\mathbf{x=\frac{7}{16}, y=\frac{68}{7} }[/tex]
Step-by-step explanation:
We need to solve [tex]\frac{3}{x}-\frac{y}{2}=2 \ and \ \frac{2}{x}+\frac{y}{4}=7[/tex]
Let:
[tex]\frac{3}{x}-\frac{y}{2}=2--eq(1)\\\frac{2}{x}+\frac{y}{4}=7--eq(2)[/tex]
Find value of x from eq(1)
[tex]\frac{3}{x}-\frac{y}{2}=2\\\frac{6-xy}{2x}=2\\ 6-xy=4x\\-4x-xy=-6\\-x(4+y)=-6\\-x=\frac{-6}{4+y}\\x= \frac{6}{4+y}[/tex]
Now put value of x in eq(2)
[tex]\frac{2}{x}+\frac{y}{4}=7\\Put \ x=\frac{6}{4+y} \\\frac{2}{\frac{6}{4+y} }+\frac{y}{4}=7\\\frac{2(4+y)}{6 }+\frac{y}{4}=7\\\frac{4+y}{3 }+\frac{y}{4}=7\\\frac{4(4+y)+3y}{12} =7\\16+4y+3y=7*12\\16+7y=84\\7y=84-16\\7y=68\\y=\frac{68}{7}[/tex]
Now putting value of y in eq(1) to find value of x
[tex]x=\frac{6}{4+y} \\Put \ y=\frac{68}{7} \\x=\frac{6}{4+\frac{68}{7} }\\x=\frac{6}{\frac{7*4+68}{7} }\\x=\frac{6}{\frac{28+68}{7} }\\x=\frac{6}{\frac{96}{7} }\\x=\frac{6*7}{96}\\x=\frac{42}{96}\\x=\frac{7}{16}[/tex]
So, Solving the given equations we get [tex]\mathbf{x=\frac{7}{16}, y=\frac{68}{7} }[/tex]
