{"id":6586,"date":"2013-12-20T19:38:37","date_gmt":"2013-12-20T19:38:37","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6586"},"modified":"2014-12-02T08:26:55","modified_gmt":"2014-12-02T08:26:55","slug":"algebra-lesson-using-two-variables-to-solve-problems","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/algebra-lesson-using-two-variables-to-solve-problems\/","title":{"rendered":"\ufeffUsing Two Variables to Solve Problems\ufeff\ufeff\ufeff"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Many equations use more than one variable, because there is more than one unknown in the sentence.\u00a0 Many times, one variable is expressed in terms of the other variable.\u00a0 Solving for one variable clears the way to solve for the other variable.<\/p>\n

Why Use Two Different Variables?<\/strong><\/p>\n

Sometimes there are two different conditions that have to be fulfilled, and each variable represents a different condition.\u00a0 For example, suppose that one condition is that there are 200 more crates of tomatoes than green peppers in a warehouse.\u00a0 Let x equal the number of crates of tomatoes, and y equal the number of crates of green peppers.\u00a0 Then the first condition would be expressed by the equation x-y =200.\u00a0 The second condition is that twice the number of crates of tomatoes is 100 more than three times the number of crates of green peppers.\u00a0 That would be expressed by the equation 2x -100 = 3y.<\/p>\n

How Are the Equations Related?<\/strong><\/p>\n

At this point, it helps to write the equations close together, so that x -y = 200 and 2x – 100 =3y.\u00a0 With the equations closer together, it is more easy to see the relationships between them.\u00a0 The equation x-y= 200 can be changed by adding y to each side so that x-y + y =200 +y.\u00a0 The -y and y cancel each other out, so that x = 200 +y.<\/p>\n

Substituting Expressions<\/strong><\/p>\n

Now that there is a value for x in terms of y as 200 + y, it can be substituted in the second equation, so that 2(200 +y) -100 =3y, or 400 + 2y – 100 =3y.\u00a0 If 300 +2y = 3y, then 300 +2y- 2y = 3y-2y, or 300 = y.\u00a0 Solving for x, if x = 200 +y, then x = 200 + 300 or x = 500.<\/p>\n

Do the Equations Check?<\/strong><\/p>\n

In Condition 1, 500 – 300 = 200.\u00a0 In Condition 2, does 2(500) – 100 = 3(300)?\u00a0 Condition 2 checks because 1000 – 100 = 900, so there are 500 crates of tomatoes and 300 crates of peppers in the warehouse.<\/p>\n

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Overview: Many equations use more than one variable, because there is more than one unknown in the sentence.\u00a0 Many times, one variable is expressed in terms of the other variable.\u00a0 Solving for one variable clears the way to solve for the other variable. Why Use Two Different Variables? Sometimes there are two different conditions that […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[1647,1753],"class_list":["post-6586","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-simultaneous-linear-equations","tag-substitution-method"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6586","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6586"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6586\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6586"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6586"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}