Question

Find an ordered pair (x,y) that satisfies both of the equations below:

2x - 3y = -5
5x - 2y = 4

Answer 1

(2,3)

Explanation:

Multiplying the first equation by 5 and the second equation by $-2$ gives

\begin{align*}

10x-15y&=-25,\\

-10x + 4y &=-8.\\

\end{align*}Adding the two equations gives $-11y = -33$, so $y=3$. Substituting $y=3$ in the first original equation gives $2x - 9 = -5$, so $2x = 4$ and $x = 2$. Therefore, the solution is $(x,y) = \boxed{(2,3)}$

Answer 2

An ordered pair(x, y) that satisfies both of the equations is (2, 3).