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dsp73
3 years ago
12

What is the solution to this system of linear equations? Y-x=6 y+x=-10

Mathematics
1 answer:
snow_tiger [21]3 years ago
8 0
\left\{\begin{array}{ccc}y-x=6\\y+x=-10\end{array}\right\ \ \ |add\ both\ sides\ of\ the\ equations\\\\2y=-4\ \ \ \ |:2\\y=-2\\\\substite\ the\ value\ of\ y\ to\ second\ equation\\\\-2+x=-10\ \ \ |+2\\x=-8

Answer:\ x=-8\ and\ y=-2

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Let speed of the boat in still water = x miles per hour

Let speed of the current = y miles per hour


When water and current both flow in same direction then effective speed will be sum of both speeds that is (x+y)


now plug the given values in formula speed=distance/time

we get equation:

(x+y)=160/8

or x+y=20...(i)


When water and current both flow in opposite direction then effective speed will be difference of both speeds that is (x-y)

now plug the given values in formula speed=distance/time

we get equation:

(x-y)=160/40

or x-y=4

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plug value of x into (i)

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plug value of y into (ii)

x=4+8=12


Hence final answer is given by:

Speed of the boat in still water = 12 miles per hour

Speed of the current = 8 miles per hour


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