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solve the system of equations the
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product of A and B is equal to 10 B * C
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is equal to 8 and a * C is equal to
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20 as usual before watching press pause
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and try to solve it the right hand sides
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of the equations are not equal to zero
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which means the left hand sides must
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also not be zero therefore each of the
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factors a b and c must not be equal to
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zero if both sides of each equation are
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not zero we can multiply these equations
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together meaning the product of the left
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hand sides of these equations should be
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equal to the product of their right hand
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sides as a result we get a * B
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multiplied B * C multiplied by a * c
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will be equal to 10 * 8 * 20 we will
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rewrite the other three equations of the
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system the order of the factors in a
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product does not matter so for
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convenience we rewrite the left hand
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side of the first equation as a * B
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multiplied by B again and we still have
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C * c meaning we have c^ 2 left all of
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this should equal 10 * 8 * 20 the
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product of a and b equals 10 so on the
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left side we get 10 * 10 * c^ 2 and all
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of this should equal 10 * 8 * 20 we
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divide both sides of the equation by 100
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and get c^ 2 on the left side and 16 on
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the right side from which c will be
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equal to plus or minus 4 let's consider
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two cases the first case is when C = -4
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and a * B = 10 B * C = 8 and a * C = 20
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substituting -4 for C into the last
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equation we find a a will be equal to -5
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we substitute the value of C into the
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third equation or substitute the found
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value into the second equation and find
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b b will be equal to -2 and C must be
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equal to -4 let's consider the second
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case where c equal POS 4 we rewrite the
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other three equations of the system
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substituting the value of C into the
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last equation we find a from the second
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or third equation we find B and C must
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be equal to 4 the solutions to the
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system are two triples of numbers a = -5
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B = -2 and C = -4 and the second triple
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is 5 2 and 4 the problem is solved if
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you understand the solution give it a
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