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Is $(2,\,1)$ a solution to this system of inequalities? $\newline$ $x + y \geq 3$ $\newline$ x > 2 $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Is (x, y) a solution to the system of linear inequalities?

Full solution

Q. Is

(2,\,1)

a solution to this system of inequalities?

\newline

x + y \geq 3

\newline

x > 2

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Inequality Satisfaction: Does the point $(2, 1)$ satisfy the inequality $x + y \geq 3$ ? $\newline$ Substitute $2$ for $x$ and $1$ for $y$ in $x + y \geq 3$ . $\newline$ $2 + 1 \geq 3$ $\newline$ $3 \geq 3$ $\newline$ Since $3 \geq 3$ is true, $(2, 1)$ satisfies the inequality $x + y \geq 3$ .
Substitute Values: Does the point $(2, 1)$ satisfy the inequality x > 2? $\newline$ Substitute $2$ for $x$ in x > 2. $\newline$ 2 > 2 $\newline$ Since 2 > 2 is false ( $2$ is not greater than $2$ ), $(2, 1)$ does not satisfy the inequality x > 2.

More problems from Is (x, y) a solution to the system of linear inequalities?

Question

Consider the following problem:

\newline

The total number of subscribers Zhang Wei has for his video page is changing at a rate of

r(t)=21-2 t

subscribers per week (where

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weeks, Zhang Wei has

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subscribers. How many subscribers does Zhang Wei have by week

20

\newline

Which expression can we use to solve the problem?

\newline

1

\newline

r(20)-r(8)+120

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\int_{20}^{20} r(t) d t

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\int_{8}^{20} r(t) d t+120

\newline

r(20)

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Anjali was given this problem:

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A person stands at a distance of

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Which equation should Anjali use to solve the problem?

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1

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\tan [d(t)]=\frac{n(t)}{12}

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d(t)=\frac{12 \cdot n(t)}{2}

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[d(t)]^{2}=12^{2}+[n(t)]^{2}

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Question

In one kind of chemical reaction, unconverted reactants change into converted reactants.

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a

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Which equation describes this relationship?

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\frac{d a}{d t}=\frac{k a}{1-a}

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\frac{d a}{d t}=k a(1-a)

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Question

Which is the set of integers greater than or equal to

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\newline

\emptyset

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\{1, 2, 3, 4, 5, 6\}

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\{0, 1, 2, 3, 4, 5, 6\}

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\{1, 6\}

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Question

The Salem Playhouse wants to make at least

\$6,800

on ticket sales this year. Currently, adults' tickets cost

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and children's tickets cost

\$16

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of adults' tickets sold

\newline

y =

the number of children's tickets sold

\newline

\newline

67 + x + 16 + y > 6,800

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67x + 16y > 6,800

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67 + x + 16 + y \geq 6,800

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67x + 16y \geq 6,800

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Question

An event planner is reserving rooms for a company-wide event. Each ballroom can hold

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841

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\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of ballrooms

\newline

y =

the number of conference rooms

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\newline

23x - 93y \geq 841

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93x + 23y \geq 841

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93x \times 23y \geq 841

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23x + 93y \geq 841

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Question

Jim is building birdhouses in shop class, and he has a total of

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\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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x =

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\newline

y =

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41x + 34y \leq 423

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Question

Craig is building a shelving unit to hold all of his shoes. A pair of work shoes takes up

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\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

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y =

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\newline

5x + 2y \leq 57

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2x + 5y < 57

\newline

2x + 5y \leq 57

\newline

5x + 2y < 57

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Question

Sasha is knitting baby items to sell at a craft fair. She has a total of

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\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of pairs of booties Sasha can knit

\newline

y =

the number of caps Sasha can knit

\newline

\newline

\newline

198x + 201y < 1,650

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198x - 201y < 1,650

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198x + 201y \leq 1,650

\newline

198x - 201y \leq 1,650

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Question

The Middletown High School softball coach is purchasing equipment for her team. She has a budget of at most

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x =

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y =

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\newline

\newline

38x - 27y < 770

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38x \times 27y \leq 770

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38x + 27y < 770

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38x + 27y \leq 770

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