Solve for a, b, c, d?
a + b = (c + d) / 2
a + c = 2b + 2d
a + d = 1.5b + 1.5c
a + b = (c + d) / 2
a + c = 2b + 2d
a + d = 1.5b + 1.5c
1 Answer
Explanation:
Multiplying the first and third equations by
#{ (2a+2b-c-d = 0), (a-2b+c-2d=0), (2a-3b-3c+2d=0) :}#
Adding the first two equations, we get:
#3a-3d=0#
Hence:
#a = d#
Substituting
#{ (a+2b-c=0), (4a-3b-3c=0) :}#
Mutiplying the first equation by
#{ (3a+6b-3c=0), (4a-3b-3c=0) :}#
Subtracting the first of these from the second, we get:
#a-9b=0#
Hence:
#a = 9b#
From a previous equation we have:
#c = a+2b = 9b+2b = 11b#
Writing
#(a, b, c, d) = (9lambda, lambda, 11lambda, 9lambda)#