Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?

y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2

Question

zarleyk2006 zarleyk2006

01-01-2021
Mathematics

Answered

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Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?

y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2

Sagot :

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torbergsenp torbergsenp · Answer 1 · 2021-01-12T11:05:02-05:00

Answer:

c

Step-by-step explanation:

c Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?

y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.

y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.

y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.

y less-than one-half x. y less-than-or-equal-to negative one-half x + 2v

MrRoyal MrRoyal · Answer 2 · 2021-12-25T08:37:02-05:00

The system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

The solution set is given as:

[tex](x,y) = (2,1)[/tex]

The above solution set is true for x + 2y ≤ 4 and 2x - y > 0, and the proof is as follows:

Substitute 2 for x and 1 for y in x + 2y ≤ 4 and 2x - y > 0.

So, we have:

[tex]\mathbf{2 + 2\times1 \le 4 }[/tex]

[tex]\mathbf{2 + 2\le 4 }[/tex]

[tex]\mathbf{4\le 4 }[/tex] --- this is true, because 4 is less than or equal to 4

Also, we have:

[tex]\mathbf{2x - y > 0}[/tex]

[tex]\mathbf{2 \times 2 - 1 > 0}[/tex]

[tex]\mathbf{4 - 1 > 0}[/tex]

[tex]\mathbf{3> 0}[/tex] --- this is also true, because 3 is greater than 0

Hence, the system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

Sagot :

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