Answer
$\left\{\left(\dfrac{11}{5},-\dfrac{3}{5}\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
y=2x-5\\
x=3y+4
\end{cases}$
Use the substitution method. Substitute the expression of $y$ from the first equation into the second to eliminate $y$ and find $x$:
$x=3(2x-5)+4$
$x=6x-15+4$
$x=6x-11$
$5x=11$
$x=\dfrac{11}{5}$
Substitute $x=\dfrac{11}{5}$ in the first equation of the given system and determine $y$:
$y=2x-5$
$y=2\left(\dfrac{11}{5}\right)-5$
$y=\dfrac{22}{5}-5$
$y=-\dfrac{3}{5}$
The solution set is:
$\left\{\left(\dfrac{11}{5},-\dfrac{3}{5}\right)\right\}$
