6 + 7 r = p w 7 r - 5 w = 5 w + 11 In the given

Question

6 + 7 r = p w 7 r - 5 w = 5 w + 11 In the given system of equations, p is a constant. If the system has no solution, what is the value of p ?

Accepted Answer

The correct answer is 10 . Solving by substitution, the given system of equations, where p is a constant, can be written so that the left-hand side of each equation is equal to 7 r . Subtracting 6 from each side of the first equation in the given system, 6 + 7 r = p w , yields 7 r = p w - 6 . Adding 5 w to each side of the second equation in the given system, 7 r - 5 w = 5 w + 11 , yields 7 r = 10 w + 11 . Since the left-hand side of each equation is equal to 7 r , setting the the right-hand side of the equations equal to each other yields p w - 6 = 10 w + 11 . A linear equation in one variable, w , has no solution if and only if the equation is false; that is, when there's no value of w that produces a true statement. For the equation p w - 6 = 10 w + 11 , there's no value of w that produces a true statement when p w = 10 w . Therefore, for the equation p w - 6 = 10 w + 11 , there's no value of w that produces a true statement when the value of p is 10 . It follows that in the given system of equations, the system has no solution when the value of p is 10 .

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