## Algebra 1

Let $x=1, y=1$. $x+y > 0$ $1+1 > 0$ $2 > 0$ (true) $x*y> 0$ $1*1 > 0$ $1 > 0$ (true) Let $x=-1, y=2$ $x+y > 0$ $-1+2 > 0$ $1 > 0$ (true) $x*y > 0$ $-1*2 > 0$ $-2 > 0$ (false) Let $x=-2, y=1$ $x+y > 0$ $-2 + 1 > 0$ $-1 > 0$ (false) $x*y > 0$ $-2*1 > 0$ $-2 > 0$ (false) Let $x=-2, y=-3$ $x+y > 0$ $-2 + (-3) > 0$ $-5 > 0$ (false) $x*y > 0$ $(-2)*(-3) > 0$ $6 > 0$ (true) The statement is sometimes true. If we let $x>0$ and $y>0$, then the statement is always true. If we let $abs(x) > abs(y) > 0$ (with either variable negative), then only part of the statement is true. If both variables are negative, then only part of the statement is true.