Which ordered pairs are solutions to the system of inequalities?
More than one answer
y ≥ x + 2
y > -5/2x - 3.
A. (0,0)
B. (-2,2)
C. (0,2)
D. (-1,6)
Answers
Answer:
C, D
Step-by-step explanation:
We can solve this graphically and analytically.
Graphically, looking at the attached image below, if we graph the two inequalities and plot the points, you can find the points which are solutions by finding the points in the overlapping area.
This obviously excludes A as it only appears in [tex]y \geq x+2[/tex]
C is included as y [tex]\geq x+2[/tex] includes the point on the line.
D is obviously a solution.
B is however not a solution because is lies on the line [tex]y = \frac{-5x}{2} - 3[/tex], which the inequality excludes.
Analytically, if we can find one of the two inequalities where it is not a solution, it is not a solution of the system.
A: (0, 0)
[tex]y \geq x+2\\0 \geq 0 + 2\\0 \geq 2\\false[/tex]
A is not a solution
B: (-2, 2)
[tex]y \geq x+2\\2 \geq -2 + 2\\2\geq 0\\true[/tex]
[tex]y > \frac{-5x}{2} -3\\2 > \frac{-5(-2)}{2} - 3\\2 > 5 - 3\\2 > 2\\false[/tex]
B is not a solution
C: (0, 2)
[tex]y \geq x+2\\2 \geq 0 + 2\\2 \geq 2\\true\\\\y>\frac{-5x}{2}-3\\2 > -3\\true[/tex]
C is a solution
D:
[tex]y \geq x + 2\\6 \geq -1 + 2\\6 \geq 1\\true\\\\y > \frac{-5x}{2} - 3\\6 > \frac{-5(-1)}{2} - 3\\6 > \frac{5}{2} - \frac{6}{2}\\6 > \frac{-1}{2}\\true[/tex]
D is a solution
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Answers
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Please check the explanation.
Step-by-step explanation:
If each linear function is given as a set of two ordered pairs, all we need is to find a slope between two lines and put one of the points in the slope- intercept form of the line equation to find the y-intercept 'b' and then writing the equation in the slope-intercept form. This is how we can generate a system of equations.
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[tex]y=mx+b[/tex]
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Please help me with this question
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Answers
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Answers
Answer:
[tex]m=\frac{5}{7}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-9, -10)
Point (-2, -5)
Step 2: Find slope m
Substitute: [tex]m=\frac{-5+10}{-2+9}[/tex]Add: [tex]m=\frac{5}{7}[/tex]And we have our final answer!
Need help ASAP pls due in 5 mins
Answers
The diagram shows four graphs match the graphs to the equations
Answers
Answer:
y=x^2 is graph D
y=1/x is graph A
otherwise, you're right
