Question

3x=8y-34y+2x=5Based on the system of equations above, what is the value of x/y?

Answer 1

To solve the given system of equations, we can solve the first equation for x, then we combine the equations

`\begin{gathered} 3x=8y-3 \\ x=(8y-3)/(3) \end{gathered}`

Then,

`\begin{gathered} 4y+2x=5 \\ 4y+2((8y-3)/(3))=5 \\ 4y+(16y-6)/(3)=5 \\ 4y+(16)/(3)y-2=5 \\ (12y+16y)/(3)=5+2 \\ (28y)/(3)=7 \\ 28y=7\cdot3 \\ y=(21)/(28) \\ y=(3)/(4) \end{gathered}`

So, y = 21/28.

Now, we use the y-value to find x.

`\begin{gathered} x=(8\cdot(21)/(28)-3)/(3)=((168)/(28)-3)/(3)=((84)/(14)-3)/(3)=((42)/(7)-3)/(3) \\ x=((42-21)/(7))/(3)=((21)/(7))/(3)=(3)/(3)=1 \end{gathered}`

Hence, the value of each variable is x = 1 and y = 3/4.