Saturday, May 30, 2020
SAT Algebra Combination vs. Substitution
Algebra is by far the most important part of SAT math. Isolating a variable is a step in many SAT math problems, depending on whether or not you use elimination strategies. Thatââ¬â¢s as it should be; after all, youââ¬â¢ve been doing that in math class for the entirety of your high school career, and itââ¬â¢s the foundational block that most other math is built on. Itââ¬â¢d be worrying if SAT math didnââ¬â¢t use a lot of algebra. Of course, that algebra comes in many shapes and forms. Some of itââ¬â¢s relatively basic, while other questions involve so many steps that little slip-upsà become a serious threat. One way to make that algebra longer is to include two variables (or more). If you have as many equations as variables, then itââ¬â¢s only a matter of using substitution or combination to get your answer. Youââ¬â¢ve seen at least one of these methods in school, of course, but you may not be equally comfortable with the two. If thatââ¬â¢s the case, then take some time getting familiar with the other; youââ¬â¢ll want to have both options to choose from during your SAT. When substitution is better If either x or y (or whatever variable you have) stands alone on one side of the equation or can be isolated really quickly, substitution is the way to go. Take a look at the example below. If , and , then what is the value of ? This is also ideal for substitution because of the other somewhat complicated stuff going onâ⬠¦ if you used combination, you might make a mistake when combining the y terms of the two equations. So letââ¬â¢s solve it. First, substitute the x out of the second equation by plugging in the right side of the first equation. And weââ¬â¢re done, right? Nope. Almost done. Remember to check what the question is asking for. In this case itââ¬â¢s the value of x, not y. But thatââ¬â¢s not hard. Just plug that value of y back in to the simpler of the two equations we were given. Now itââ¬â¢s done. When combination is better If thereââ¬â¢s one variable that has the same coefficient in both equations, then combination is probably a good idea. Or better yet, if the coefficient in one equation is the negative of that in the other equation, then weââ¬â¢re set. What does that mean? Good combination questions look like this: If , and , then what is the value of ? With that 3x in one equation and -3x in the other equation, itââ¬â¢s pretty quick to cancel them out. So letââ¬â¢s line up the two equations over each other, then combine them into one. If you fell for that trap the first time, I hope youââ¬â¢re not going to do it again. Find x. And now weââ¬â¢re done. Use whichever method is easier on the day of your SAT While youââ¬â¢re practicing, itââ¬â¢s a good idea to try to vary which method you use, so you have both tools at your disposal. But on the day of your test, you donââ¬â¢t want to spend any time deliberating. Just pick whichever seems easiest and go for it.
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