3 a – 7b = 4d – 9
–4c + 10a = 6b + 7
–2a + 3c – 4d = 10Given the system of equations above, what is the value of –10a – 2b + 2c ?Here’s How to Crack It
Notice that the test writers have made this problem harder by mixing up the variables. Your first step is to
line up the variables on the left side of the equation and arrange them in alphabetical order; move the
constants to the right side of the equation. Combine like terms in each equation, and use a place holder for
any variables that are missing in each equation.
Step 1: 3 a – 7b + 0c – 4d = –9
10 a – 6b – 4c + 0d = 7
–2a + 0b + 3c – 4d = 10“Nothing” is Helpful
In these equations, the
place holders are 0c,
0 d, and 0b respectively.
Because 0 times any
number is 0, nothing has
been added to the equa-
tion; these 0’s are simply
acting as placeholders, so
that all of the variables
line up vertically. You may
also choose to leave these
areas blank.Once you have the variables aligned, complete this problem just like the previous problem by adding and
subtracting the equations until you get something that looks like the expression in the question.
IF YOU ADD: