Consider the system:
2 answers:
Answer:
Step-by-step explanation:
In this problem, we have the following linear equations:
y=3x+5
y=ax+b
We know that a linear equation is an equation for a line. In a system of linear equations, two or more equations work together.
1. What values for a and b make the system inconsistent?
A system is inconsistent if and only if the lines are parallel in which case the system has no solution. This is illustrated in the first Figure bellow. Two lines are parallel if they share the same slope. So, the system is inconsistent for:
a=3
for any value of b
2. What values for a and b make the system consistent and dependent?
A system is consistent if and only if the lines are the same in which case the system has infinitely many solutions. This is illustrated in the second Figure bellow. So, the system is consistent and dependent for:
a=3 and b=5
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Answer:
The speed of jogger in uphills is 4 mile per hour
And The speed of jogger in downhills is 10 mile per hour
Step-by-step explanation:
Given as :
The distance cover by jogger in downhill (Dd) = 5 miles
The distance cover by jogger in uphill (Du) = 2 miles
The time taken by jogger in downhill (Td) = T hour
The time taken by jogger in uphill (Tu) = T hour
Let The speed of jogger in uphills (Su) = x mph
So ,The speed of jogger in downhills (Sd) =( x + 6 ) mph
∵, Time =
So, Tu =
Or, T = h
And Td =
Or, T = h
∵ Time duration of both is same
∴ =
Or, 2 × (x + 6) = 5x
Or, 2x + 12 = 5x
So, 12 = 3x
∴ x = = 4 mph
And x + 6 = 4 + 6 = 10 mph
Hence The speed of jogger in uphills is 4 mile per hour
And The speed of jogger in downhills is 10 mile per hour Answer