{"id":1000,"date":"2013-04-03t09:00:17","date_gmt":"2013-04-03t09:00:17","guid":{"rendered":"\/\/www.catharsisit.com\/sat\/?p=1000"},"modified":"2018-10-24t03:30:21","modified_gmt":"2018-10-24t10:30:21","slug":"sat-algebra-combination-vs-substitution","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/","title":{"rendered":"sat algebra: combination vs. substitution"},"content":{"rendered":"

algebra is by far the most important part of sat math. isolating a variable is a step in many<\/i> sat math problems, depending on whether or not you use elimination strategies. that\u2019s as it should be; after all, you\u2019ve been doing that in math class for the entirety of your high school career, and it\u2019s the foundational block that most other math is built on. it\u2019d be worrying if sat math didn\u2019t<\/i> use a lot of algebra.<\/p>\n

of course, that algebra comes in many shapes and forms. some of it\u2019s relatively basic, while other questions involve so many steps that little slip-ups<\/a>\u00a0 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 it\u2019s only a matter of using substitution or combination to get your answer.<\/p>\n

you\u2019ve seen at least one of these methods in school, of course, but you may not be equally comfortable with the two. if that\u2019s the case, then take some time getting familiar with the other; you\u2019ll want to have both options to choose from during your sat.<\/p>\n

 <\/p>\n

when substitution is better<\/h2>\n

if either x<\/i> or y <\/i>(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.<\/p>\n

if <\/i>\"x=11-y\", and <\/i>\"y^2=x+(y-1)^2\", then what is the value of <\/i>\"x\"?<\/i><\/p>\n

this is also ideal for substitution because of the other somewhat complicated stuff going on\u2026 if you used combination, you might make a mistake when combining the y <\/i>terms of the two equations.<\/p>\n

so let\u2019s solve it.<\/p>\n

first, substitute the x <\/i>out of the second equation by plugging in the right side of the first equation.<\/p>\n

\"y^2=x+(y-1)^2\"<\/p>\n

\"y^2=(11-y)+(y-1)^2\"<\/p>\n

\"y^2=(11-y)+(y^2-2y+1)\"<\/p>\n

\"y^2=11-y+y^2-2y+1\"<\/p>\n

\"y^2=12-3y+y^2\"<\/p>\n

\"0=12-3y\"<\/p>\n

\"3y=12\"<\/p>\n

\"y=4\"<\/p>\n

and we\u2019re done, right?<\/p>\n

nope. almost <\/i>done.<\/p>\n

remember to check what the question is asking for. in this case it\u2019s the value of x<\/i>, not y.<\/i><\/p>\n

but that\u2019s not hard. just plug that value of y <\/i>back in to the simpler of the two equations we were given.<\/p>\n

\"x=11-y\"<\/p>\n

\"x=11-(4)\"<\/p>\n

\"x=7\"<\/p>\n

now it\u2019s done.<\/p>\n

 <\/p>\n

when combination is better<\/h2>\n

if there\u2019s 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 we\u2019re set.<\/p>\n

what does that mean? good combination questions look like this:<\/p>\n

if <\/i>\"3x-{y\/2}=19\", and <\/i>\"5y-3x+1=0\", then what is the value of <\/i>\"x\"?<\/i><\/p>\n

with that 3x <\/i>in one equation and -3x <\/i>in the other equation, it\u2019s pretty quick to cancel them out. so let\u2019s line up the two equations over each other, then combine them into one.<\/p>\n

\"3x-{y\/2}=19\"<\/p>\n

\"5y-3x+1=0\"<\/p>\n

\"3x-{y\/2}=19\"<\/p>\n

\"-3x+5y+1=0\"<\/p>\n

\"5y+1-{y\/2}=19\"<\/p>\n

\"5y-{y\/2}=18\"<\/p>\n

\"10y-y=36\"<\/p>\n

\"9y=36\"<\/p>\n

\"y=4\"<\/p>\n

if you fell for that trap the first time, i hope you\u2019re not going to do it again. find x.<\/i><\/p>\n

\"3x-{y\/2}=19\"<\/p>\n

\"3x-(4\/2)=19\"<\/p>\n

\"3x-(2)=19\"<\/p>\n

\"3x=21\"<\/p>\n

\"x=7\"<\/p>\n

and now we\u2019re done.<\/p>\n

 <\/p>\n

use whichever method is easier on the day of your sat<\/h2>\n

while you\u2019re practicing, it\u2019s 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 don\u2019t want to spend any time deliberating. just pick whichever seems easiest and go for it.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

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. that\u2019s as it should be; after all, you\u2019ve been doing that in math class for the entirety of your high school career, and it\u2019s […]<\/p>\n","protected":false},"author":42,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[40,81],"ppma_author":[24883],"acf":[],"yoast_head":"\nsat algebra: combination vs. substitution - magoosh blog | high school<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/\" \/>\n<meta property=\"og:locale\" content=\"en_us\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"sat algebra: combination vs. substitution\" \/>\n<meta property=\"og:description\" content=\"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. that\u2019s as it should be; after all, you\u2019ve been doing that in math class for the entirety of your high school career, and it\u2019s […]\" \/>\n<meta property=\"og:url\" content=\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/\" \/>\n<meta property=\"og:site_name\" content=\"magoosh blog | high school\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/magooshsat\/\" \/>\n<meta property=\"article:published_time\" content=\"2013-04-03t09:00:17+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-10-24t10:30:21+00:00\" \/>\n<meta name=\"author\" content=\"lucas fink\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:site\" content=\"@magooshsat_act\" \/>\n<meta name=\"twitter:label1\" content=\"written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"lucas fink\" \/>\n\t<meta name=\"twitter:label2\" content=\"est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"article\",\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/#article\",\"ispartof\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/\"},\"author\":{\"name\":\"lucas fink\",\"@id\":\"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/c06e6a007d0b81117c00610ed88b6c7d\"},\"headline\":\"sat algebra: combination vs. substitution\",\"datepublished\":\"2013-04-03t09:00:17+00:00\",\"datemodified\":\"2018-10-24t10:30:21+00:00\",\"mainentityofpage\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/\"},\"wordcount\":682,\"commentcount\":2,\"publisher\":{\"@id\":\"\/\/www.catharsisit.com\/hs\/#organization\"},\"keywords\":[\"sat averages\",\"sat math section\"],\"articlesection\":[\"sat\"],\"inlanguage\":\"en-us\",\"potentialaction\":[{\"@type\":\"commentaction\",\"name\":\"comment\",\"target\":[\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/#respond\"]}]},{\"@type\":\"webpage\",\"@id\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/\",\"url\":\"\/\/www.catharsisit.com\/hs\/sat\/sat-algebra-combination-vs-substitution\/\",\"name\":\"sat algebra: combination vs. substitution - 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