Question

Direction: Determine whether the given point is a solution to the given system of linear inequalities.

Answer 1

Answer:

The given point is a solution to the given system of inequalities.

Step-by-step explanation:

Again, we can substitute the coordinates of the given point into the system of inequalities. We know that the x-coordinate and y-coordinate of $(3,2)$ are $x=3$ and $y=2$, respectively.

Plugging these values into the first inequality, $y\leq x+3$, gives us $2\leq 3+3$, which simplifies to $2\leq 6$. This is a true statement, so the given point satisfies the first inequality. We still need to check if it satisfies the second inequality though, because if it doesn't, it won't be a solution to the system.

Plugging the coordinates into the second inequality, $y\geq -x+3$, gives us $2\geq -3+3$, which simplifies to $2\geq 0$. This is also a true statement, so the given point satisfies the second inequality as well. Therefore, $\bold(\bold3\bold,\bold2\bold)$ is a solution to the given system of inequalities since it satisfies all of the inequalities in the system. Hope this helps!