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

$\begin{gathered} 3x=8y-3 \\ x=\frac{8y-3}{3} \end{gathered}$

Then,

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

So, y = 21/28.

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

$\begin{gathered} x=\frac{8\cdot\frac{21}{28}-3}{3}=\frac{\frac{168}{28}-3}{3}=\frac{\frac{84}{14}-3}{3}=\frac{\frac{42}{7}-3}{3} \\ x=\frac{\frac{42-21}{7}}{3}=\frac{\frac{21}{7}}{3}=\frac{3}{3}=1 \end{gathered}$

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