Find an ordered pair $(x,y)$ that satisfies both of the equations below: \begin{align*} 2x - 3y &= -5,\\ 5x - 2y &= 4. \end{align*}
One way to do that is to use the elimination method, where I multiply one or both equations by some factor and then add or subtract them to eliminate one of the variables. For example, if I multiply the first equation by $5$ and the second equation by $-2$, I get: \begin{align*} 10x - 15y &= -25,\\ -10x + 4y &= -8. \end{align*} Then, if I add these two equations, I get: \begin{align*} -11y &= -33. \end{align*} Solving for $y$, I get: \begin{align*} y &= 3. \end{align*} Now that I know $y = 3$, I can plug it into either of the original equations to find $x$. I'll use the first one: \begin{align*} 2x - 3(3) &= -5,\\ 2x - 9 &= -5,\\ 2x &= 4,\\ x &= 2. \end{align*} So, the ordered pair that satisfies both equations is $(2,3)$.

