Answer
$( 1,1)$
Work Step by Step
To eliminate y, multiply both equations with numbers so the coefficient of y is $\pm 6:$
$\left\{\begin{array}{llll}
2x & +3y & =5 & /\times 2\\
3x & +2y & =5 & /\times(-3)
\end{array}\right.$
$\left\{\begin{array}{llll}
4x & +6y & =10 & \\
-9x & -6y & =-15 &
\end{array}\right.$
... add and solve ...
$-5x=-5\qquad/\div 5$
$x=1$
Back substitute into one of the initial equations:
$3x+2y=5$
$3(1)+2y=5\qquad /-3$
$2y=2\qquad /\div 2 $
$y=1$
Solutions are ordered pairs (x,y):
$( 1,1)$
Check graphically by graphing both lines in the same window and determining the intersection (see image).
