Question 107615: Kindly show me step by step how to do this:
Given that a - b = 10, c - d = 14, and 7a + 5d = 23, what is the value of ac - bd? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! a-b=10-------------------eq1
c-d=14---------------------eq2
7a+5d=23---------------------eq3
multiply each term in eq1 by c and we get:
ac-bc=10c--------------------eq1a
multiply each term in eq2 by b and we have
bc-bd=14b---------------------eq2a
add eq 1a and eq2a and we get:
ac-bd=14b+10c-------eq2c
but from eq1:
b=a-10---eq1b
and from eq2:
c=14+d---eq2b
substitute eq1b and eq2b into eq2c:
ac-bd=14(a-10)+10(14+d) get rid of parens (distributive law):
ac-bd=14a-140+140+10d collect like terms
ac-bd=14a+10d=2(7a+5d) but from eq3, we know that 7a+5d=23, so:
ac-bd=2(23) or
ac-bd=46
