Respuesta :
Answer:
D) (5,0)
Step-by-step explanation:
-5x + 4 ≤ y
-25 + 5 ≤ 0
-20 ≤ 0
y ≤ 2x + 2
0 ≤ 2(5) + 2
0 ≤ 27
Both equations are satisfying by substituting (5, 0) in the system of inequalities.
Option (D) is correct answer.
What are system of inequalities?
"A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system."
Given
System of inequalities graphed equation
y ≤ 2x + 2.................(1)
y ≥ -5x + 4................(2)
Explanation for correct option:
(D) (5, 0)
Substituting the point in equation 1 and 2
y ≤ 2x + 2
⇒ 0 ≤ 2(5) + 2
⇒ 0 ≤ 27
It is true
y ≥ -5x + 4
⇒ 0 ≥ -5(5) + 4
⇒ 0 ≥ -25 + 4
⇒ 0 ≥ -21
It is also true
In this option Both equations are satisfying by substituting (5, 0)
Explanation for other options:
(A) (1, 6)
Substituting the point in equation 1 and 2
y ≤ 2x + 2
⇒ 6 ≤ 2(1) + 2
⇒ 6 ≤ 4
It is false
y ≥ -5x + 4
⇒ 6 ≥ -5(1) + 4
⇒ 6 ≥ -5 + 4
⇒ 6 ≥ -1
It is true
Both equations are not satisfying by substituting (1, 6)
(B) (-6, 0)
Substituting the point in equation 1 and 2
y ≤ 2x + 2
⇒ 0 ≤ 2(-6) + 2
⇒ 0 ≤ -10
It is false
y ≥ -5x + 4
⇒ 0 ≥ -5(-6) + 4
⇒ 0 ≥ 30 + 4
⇒ 0 ≥ 34
It is false
Both equations are not satisfying by substituting (-6, 0)
(C) (0, 5)
Substituting the point in equation 1 and 2
y ≤ 2x + 2
⇒ 5 ≤ 2(0) + 2
⇒ 5 ≤ 2
It is false
y ≥ -5x + 4
⇒ 5 ≥ -5(0) + 4
⇒ 5 ≥ 0 + 4
⇒ 5 ≥ 4
It is true
Both equations are not satisfying by substituting (0, 5)
Hence, Both equations are satisfying by substituting (5, 0) in the system of inequalities given.
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