1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrej [43]
3 years ago
10

Which ordered pairs are in the solution set of the system of linear inequalities?

Mathematics
1 answer:
Anastaziya [24]3 years ago
8 0
<h3>Answer: Choice A.  (2,2), (3,1), (4,2)</h3>

==========================================================

Explanation:

The graph of y \ge -\frac{1}{3}x+2 has the boundary y = (-1/3)x+2 which is a solid line. This line goes through (0,2) and (3,1). We shade above the boundary because of the "greater than" sign.

The graph of y < 2x+3 has a dashed boundary line of y = 2x+3, and we shade below the boundary because of the "less than" sign.

The two regions overlap in the upper right corner where it's shaded in the darkest color. The points (2,2), (3,1) and (4,2) are in this upper right corner region. If we plug the coordinates of each point into each inequality, then we'll get true statements.

For instance, let's try (x,y) = (2,2) into the first inequality

y \ge -\frac{1}{3}x+2\\\\2 \ge -\frac{1}{3}(2)+2\\\\2 \ge -\frac{2}{3}+2\\\\2 \ge -\frac{2}{3}+\frac{6}{3}\\\\2 \ge \frac{-2+6}{3}\\\\2 \ge \frac{4}{3}\\\\2 \ge 1.33\\\\

Which is true since 2 is indeed larger than 1.33, so that confirms (2,2) is in the shaded region for y \ge -\frac{1}{3}x+2\\\\

Let's check the other inequality as well

y < 2x+3\\\\2 < 2(2)+3\\\\2 < 4+3\\\\2 < 7\\\\

That works too. So (2,2) is in BOTH shaded regions at the same time; hence, it's a solution to the system. You should find that (3,1) and (4,2) work for both inequalities also. This will confirm choice A is the answer.

--------------------------------

Extra info (optional section)

A point like (3,-1) does not work for the first inequality as shown below

y \ge -\frac{1}{3}x+2\\\\-1 \ge -\frac{1}{3}(3)+2\\\\-1 \ge -1+2\\\\-1 \ge 1\\\\

Since -1 is neither equal to 1, nor is -1 larger than 1 either. The false statement at the end indicates (3,-1) is not a solution to that inequality.

Based on the graph, the point (3,-1) is not above the blue solid boundary line. All of this means we can rule out choice B.

You should find that (1,-2) is a similar story, so we can rule out choice C. Choice D can be ruled out because (2,0) is not a solution to the first inequality.

You might be interested in
PLEASE HELP!! WILL GIVE BRAINLIEST!
Jobisdone [24]
No baby daddy said no
8 0
3 years ago
Anwser the question for brainlist
klasskru [66]

Answer:

there's no question, pal

Step-by-step explanation:

27.9333, use a calculator.

6 0
3 years ago
Solve this equation |x-4|+4&gt;9
g100num [7]
|x - 4| + 4 > 9 \\ |x - 4| >5 \\ x - 4 > 5 \: or \: x - 4 < - 5 \\ x > 9 \: or \: x < - 1
Btw it's an inequality not an equation
3 0
3 years ago
What is negative 7 minus negative 4
Nimfa-mama [501]

Answer:

-7-(-4)= -3

Step-by-step explanation:

Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive.

3 0
3 years ago
Read 2 more answers
Your friend has a bag of 20 marbles. Seven
Elis [28]

Answer:

20%

Step-by-step explanation:

First, I added them up. From the things we know, blue, red, green, yellow combined equals 16 marbles. 20-16 equals 4. So there are 4 white marbles. 4/20 times 5 equals 20/100. So the percent of the marbles that are white is 20%.

6 0
3 years ago
Read 2 more answers
Other questions:
  • The system shown is____.<br>equivalent<br>independent<br>inconsistent
    7·1 answer
  • Is 25/99 a repeating or terminating decimal?
    15·1 answer
  • When 18 is reduced by two-thirds of a number the result is 12 find the number
    11·1 answer
  • Find P(C|Y) from the information in the table.<br><br><br><br> To the nearest tenth, P(C|Y) =
    11·1 answer
  • a sign at a store said all purchases were 40% off.which is another way this nuber could have been written A .1/5 off B.1/4 off C
    5·1 answer
  • Mrs Perry, shares out 35 biscuits between gemma and zak in the ratio of 1:6. How many biscuits does gemma and zak get?
    14·1 answer
  • 3.a. Solve the following equations.<br>​
    7·1 answer
  • Which equation would be the easiest to solve first by using the substitution method? EXPLAIN WHY
    11·1 answer
  • What is an expected outcome called
    7·1 answer
  • Investor Lucas just bought a large amount of stock in Company Y. What may have motivated his behavior? (5 points)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!