Answers:
So the solution is (x,y) = (4, -1)
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Work Shown:
6x + 7y = 17
6x + 7( y ) = 17
6x + 7( -3x+11 ) = 17 ... replace every copy of y with -3x+11
6x - 21x + 77 = 17
-15x = 17-77
-15x = -60
x = -60/(-15)
x = 4
We'll use this x value to find y
y = -3x+11
y = -3(4)+11 ... replace x with 4
y = -12+11
y = -1
We have x = 4 and y = -1 pair up together to give us the solution (x,y) = (4, -1)
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To check the solution, we plug x = 4 and y = -1 into each equation
Plugging the values into the first equation leads to...
y = -3x+11
-1 = -3(4)+11
-1 = -1
This is effectively already done in the last part of the previous section. But it doesn't hurt to verify like this regardless.
We'll need to verify the second equation as well.
6x + 7y = 17
6(4) + 7(-1) = 17
24 - 7 = 17
17 = 17
We get a true equation, so the solution is confirmed with both equations. Overall, the solution to the system of equations is confirmed. This system is independent and consistent.
The quadrant of the coordinate plane (2,-3) Will be located in is quadrant IV (4)
Answer:
Smallest rate for the train is 50 mph and largest is 60 mph.
For the bus it is 25 and 30 mph.
Step-by-step explanation:
If the speed of the train is 2x then speed of the bus is x mph, and the train travels twice as far as the bus in a given time.
Distance = speed * time
For the largest rate:
d = 2x * 0.5 for the train
x = d
0.5d = x for the bus
d - 0.5d = 15
0.5d = 15
d = 30
So the rate for the train = 30 / 0.5 = 60 mph.
In a similar fashion we can show that the smallest rate for the train is
25/ 0.5 = 50 mph.
Because mushrooms absorb water (giving it less flavor).
