16(1257). Construct the graph of the equation:

a) $(x-2)(y+3)=0 ; \quad$ b) $x^{2}+x y=0$.
Solution. a) Since the product is equal to zero when at least one of the factors is equal to zero, the equation $(x-2) \times$ $\times(y+3)=0$ is satisfied by pairs of numbers $x=2, y$ - any number or $x$ - any number, $y=-3$. Therefore, the graph of the equation $(x-2)(y+3)=0$ consists of two lines $x=2$ and $y=-3$ (Fig. 10).

b) Let's factor the left side of the equation $x^{2}+x y=0$. We will have $x(x+y)=0$, from which $x=0$ or $y=-x$. Therefore, the graph of the equation $x^{2}+x y=0$ consists of two lines $x=0$ and $y=-x$ (Fig. 11).

Note. It is advisable to solve problems $1200,1209,1210$ from the textbook [4] simultaneously with this problem.