Solving Systems of Equations
Occasionally the SAT will give you two equations and ask
you to determine the value of a particular variable or some other
equation or expression. For example, the SAT might ask :
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If
3x + 4y = 32 and 2y – x =
6, then x – y = ? |
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The best way to answer this type of question is to use
a type of substitution method: solve for one variable and then substitute
that value into the other equation. Since the x in
the second equation has no coefficient next to it, it will be easier
to solve for that variable. All it takes is a little reorganizing:
Now, all we have to do is plug 2y –
6 into the value for x in the
first equation:
Now, we have only one variable to deal with in
the equation, and we can easily solve for it:
Once we know the value of y,
we can plug that value into either equation to solve for x.
Since y = 5 and x =
4, x – y = 4 – 5 = –1.
When you solve problems that deal with systems of equations,
always be careful of two things.
- Make sure you solve for the first variable
in its lowest form (solve for x rather than 2x).
- Answer the question the SAT asks. For example, in the
sample above, the question asked for the value of x – y.
But it’s certainly possible that after doing all the work and figuring
out that x = 4, you might forget to carry out the final simple
operation 4 – 5 = –1 and think that the answer is 4.
You can be sure that the test will try to trick you by including 4 as
one of its answer choices.
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