Question

Please answer thank you

Answer 1

Yes, it is the solution

Explanation:

You are given the system of two inequalities

`\left\{\begin{array}{l}y\le -3x+4\\ \\y>x^2+3x-2\end{array}\right.`

To check whether point (0,4) is the solution to this system, substitute x=0 and y=4 into each inequality:

1.

`4\le -3\cdot 0+4\\ \\4\le 4 \ [\text{true}]`

2.

`4>0^2+3\cdot 0-2\\ \\4>0+0-2\\ \\4>-2\ [\text{true}]`

Since the coordinates of the point (0,4) satisfy both inequalities, the point (0,4) is the solution to the system

Answer 2

Yes, (0,4) is a solution

Explanation:

We have to plug in 0 in x and 4 in y IN BOTH THE INEQUALITIES.

IF BOTH ARE TRUE, then the system of inequalities is TRUE.

Let's check:

y ≤ -3x+4

4 ≤ -3(0)+4

4 ≤ 4

Is 4 less than OR equal to 4? Yes. THis is satisfied.

Now, checking 2nd one:

y > x^2 + 3x - 2

4 > (0)^2 + 3(0) - 2

4 > -2

Is 4 greater than -2? Yes, it is. So this is satisfied as well.

Hence, (0,4) is a solution to the system of inequalities shown.