{"id":7042,"date":"2014-06-09T16:25:24","date_gmt":"2014-06-09T16:25:24","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=7042"},"modified":"2014-12-02T08:25:29","modified_gmt":"2014-12-02T08:25:29","slug":"math-review-of-solving-systems-with-substitution","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/06\/09\/math-review-of-solving-systems-with-substitution\/","title":{"rendered":"Math Review of Solving Systems with Substitution"},"content":{"rendered":"

Overview<\/h3>\n

One way to solve systems of equations with more than one variable is to substitute values of one variable for another.\u00a0 Suppose that a variable y is equal to 2x.\u00a0 One way to solve the equation x + y = 12 is by substituting x + 2x = 12 so that x is equal to 4 and y is equal to 2\u22194, or 8.<\/p>\n

Substituting Variables<\/h3>\n

The simplest form of substitution is when one variable is listed in terms of the other, as in the example above.\u00a0 Suppose that y = x + 3 and x + y = 13.\u00a0 Then x + x + 3 = 13, so 2x equals 10, or x equals 5.\u00a0 If x equals 5, then x +3 equals 8 and 5 + 8 = 13.\u00a0 Checking the equation by replacing the variables with numbers fulfills both conditions.<\/p>\n\n\n\n
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Figure 1: Substituting values for variables is like fitting together the pieces of a puzzle.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Substituting Quantities<\/h3>\n

Another form of substitution occurs when two different variables are given in terms of a third, as when a mixture or solution has one quantity of one variable and another quantity of another variable and the parts added together make a given amount.\u00a0 Suppose that a fruit punch contains 3 parts apple juice to 1 part cranberry juice.\u00a0 If 5 gallons of punch are made, how many quarts of apple juice and how many quarts of cranberry juice will it take?\u00a0 There are 2 substitutions that take place in this problem.\u00a0 If there are 4 quarts in a gallon, then there are 20 quarts in 5 gallons.\u00a0 Let a stand for apple juice and c for cranberry juice.\u00a0 Then a = 3c, and 3c + c = 20.\u00a0 If 4c = 20 then c = 5, and 3c = 15.<\/p>\n\n\n\n
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Figure 2:\u00a0Combining quantities is another way to use substitution.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Substituting Equations<\/h3>\n

Another form of substitution occurs when two equations are equivalent to the same variable.\u00a0 Suppose that there are 2 lines, one with y = 3x +2 and one with y = -4x – 5.\u00a0 Will they intersect at any point in the coordinate plane?\u00a0 One of the ways to solve this problem is to set 3x + 2 = -4x – 5. With 3x + 4x = -2 + -5, 7x = -7, so x = -1.\u00a0 Choosing the first equation, the y coordinate is -1.<\/p>\n\n\n\n
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Figure 3:\u00a0 Use substitution to find out where lines intersect.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Equations with No Solution<\/h3>\n

Suppose the lines in question were y = 3x + 3 and y = 3x + 2.\u00a0 Will those lines intersect at any point?\u00a0 As before, 3x + 3 = 3x + 2.\u00a0 In solving the equation the x cancels out, so that the resulting equation gives a nonsense statement 0 = -1. \u00a0The nonsense statement means that there is no point that the lines intersect.\u00a0 The lines are parallel.<\/p>\n

Figure 4:\u00a0 If there is no solution, graphed lines are parallel.<\/p>\n

\"monohybridcross\"<\/a><\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Xenia, OH: visit Tutoring in Xenia, OH<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview One way to solve systems of equations with more than one variable is to substitute values of one variable for another.\u00a0 Suppose that a variable y is equal to 2x.\u00a0 One way to solve the equation x + y = 12 is by substituting x + 2x = 12 so that x is equal […]<\/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":[2699,1752],"class_list":["post-7042","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-graphic-representations","tag-substitution"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=7042"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7042\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=7042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=7042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=7042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}