is the point (- 3, 10) a solution to the system of inequalities shown below? explain your answer. if not…

Explanation:

Step1: Substitute into first - inequality

Substitute (x=-3) and (y = 10) into (-5x + 3y\leq45). (-5\times(-3)+3\times10=15 + 30=45). Since (45\leq45), the point satisfies the first inequality.

Step2: Substitute into second - inequality

Substitute (x=-3) and (y = 10) into (2x+3y>24). (2\times(-3)+3\times10=-6 + 30=24). Since (24\not>24), the point does not satisfy the second inequality. So ((-3,10)) is not a solution to the system of inequalities.

Step3: Find a solution

Let's solve the system by first subtracting the first inequality (-5x + 3y\leq45) from the second (2x+3y>24) to eliminate (y). ((2x + 3y)-(-5x + 3y)>24 - 45), (2x+3y + 5x-3y>-21), (7x>-21), (x>-3). Let (x = 0), then substitute into (2x+3y>24), we get (3y>24), (y > 8). Let (y=9). A solution could be ((0,9)).

Answer:

The point ((-3,10)) is not a solution. A solution is ((0,9))