Why are there two possibilities? Because 4^2 = 16 and (–4)^2 = 16. Let’s try
graphing both on the number line.
This time, the circles are filled in because x can be greater than or equal to 4
and less than or equal to –4.
Systems of Equations
Sometimes the SAT will throw not one, but two equations at you. Most of the
time, each equation will have two variables. We call this a system of equations,
and this might seem, at first glance, like double the work. But the fact that there
are two equations actually makes solving for one or both of the variables easier.
There are two methods for tackling this kind of problem. Sometimes the first
method is easier, sometimes the second. You should know how to use both of
them.
Say you’re supposed to solve for x in this system:
2 x + 3y = 6
5 x + 8y = 11
Systems of equations are my pride and joy and what keep me going on the tough days. No, seriously though, you can use these guys foralmost anything.
—Samantha
FIRST METHOD: ELIMINATION
Keep them stacked up, then multiply or divide the equations to make the
coefficients of either the x’s or the y’s equal. Sometimes they’re equal when you
start out. But this time we’re not so lucky. Let’s say we go with the x’s. In order
to make the coefficients equal, multiply the top equation by 5 and the bottom
equation by 2.
5 (2x + 3y) = (6) 5 2 (5x + 8y) = (11) 2You end up with:10 x + 15y = 30