.
If you just know what is the systems of equations, then you can write, based on the condition
x + y = 11302 (1)
x - y = 2854 (2)
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Now add the equations, and you will get
2x = 11302 + 2854 = 14156; hence, x = 14156/2 = 7078.
ANSWER. The longer river length is 7078 km; The other river is 7078 - 2854 = 4224 km.
Solved.
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If you don't know what is the system of equations, you may solve the problem by different way.
Longer river length + other river length = 11302
x + (x - 2854) = 11302
2x = 11302 + 2854 = 14156
x = 14156/2 = 7078 km
obtaining the same answer.
Solved by two ways, to provide you the best knowledge.
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Regarding the method of solution with system of equation, know that this system is SIMPLEST of this kind.
To gain an experience solving such systems (and such problems), see the lesson
- Word problems that lead to a simple system of two equations in two unknowns
in this site.