Answer
$(\displaystyle \frac{1-3y}{2}, y)$
Work Step by Step
Remove the fractions by multiplying
the second equation with $2$,
(common denominator).
$\left\{\begin{array}{llll}
2x & +3y & =1 & \\
-2x & -3y & =-1 & /\times 4
\end{array}\right.$
... add to eliminate x, solve for y...
$0=0$
$y$ can be ANY real number
(the system is consistent, but there are infinitely many solutions)
(we expect the graphs to be the same)
Express x in terms of y from any of the initial equations:
$2x+3y=1\qquad/-3y$
$2x=1-3y\qquad/\div 2$
$x=\displaystyle \frac{1-3y}{2}$
solution: $(\displaystyle \frac{1-3y}{2}, y)$
Check graphically by graphing both lines in the same window and
confirming that both equations have the same graph (see image).
