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Harrizon [31]
3 years ago
9

Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2 y > –2

Mathematics
1 answer:
sladkih [1.3K]3 years ago
8 0

Answer:

False

Step-by-step explanation:

4x + y < 2

y > –2

Substitute the point into the inequalities and see if they are true

4(4) + 2 < 2

16+2 < 2

18 <2  False

2 > –2  True

Since one is false the point is not a solution

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EXPLANATION

Given information

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\begin{gathered} \text{ The perimeter of a rectangular field = 2\lparen l + w\rparen} \\ \text{ where l =length, and w = width} \end{gathered}

Step 2: Substitute the given data into the formula in step 1

\begin{gathered} \text{ Perimeter = 2 \lparen l + w\rparen} \\ \text{ Perimeter = 372 yards} \\ \text{ width = 87 yards} \\ \text{  372 = 2\lparen l + 87\rparen} \\ \text{ Divide both sides by 2} \\ \text{ }\frac{372}{2}\text{ = }\frac{2}{2}(l\text{ + 87\rparen} \\ 186\text{ = l + 87} \\ \text{  subtract 87 from each sides of the equation} \\ \text{ 186 - 87 = l + 87 - 87} \\ \text{  99 = l} \\ l\text{ = 99 yards} \end{gathered}

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