{"id":9076,"date":"2017-01-11T16:12:39","date_gmt":"2017-01-11T16:12:39","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=9076"},"modified":"2017-01-12T18:04:36","modified_gmt":"2017-01-12T18:04:36","slug":"math-review-of-solving-systems-by-substitution","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2017\/01\/11\/math-review-of-solving-systems-by-substitution\/","title":{"rendered":"Math Review of Solving Systems by Substitution"},"content":{"rendered":"

Overview<\/strong><\/h4>\n

One of the ways to solve systems of equations is by graphing the equations.\u00a0 However, graphing the equations is not always the most accurate method to solve them.\u00a0 If one variable in a system is represented in terms of the other variable in the system, the systems can be solved by substitution.<\/p>\n

Using Substitution<\/strong><\/h4>\n

Suppose one of the equations in the system is x + y = 5 and the other equation is x = y +1.\u00a0 The expression y +1 can be substituted for x, so that y +1 +y =5.\u00a0 Then, there is just one variable so that 2y +1 =5, 2y +1 -1 = 5-1, or 2y = 4, or y =2.\u00a0 In order to check, substitute the value of y to solve for x, such that x +2 = 5, or x +2-2 = 5-2, or x = 3.\u00a0 Check the second equation also, so that 3 =2 +1. That is the way to use substitution to solve a system of equations.<\/p>\n

<\/h4>\n

Isolating the Variables<\/strong><\/h4>\n

Sometimes, the variables cannot be isolated as easily in a system of equations, but the system of substitution can still be used.\u00a0 Suppose the equations were x-2y = 8 and 2x +y = 8.\u00a0 The first equation can be rearranged such that x = 8 +2y.\u00a0 Using substitution, the second equation then becomes 2(8 +2y) +y =8, or 16 +4y +y =8.\u00a0 As before, there is only one variable, such that 5y = 8-16 or 5y=-8, or y = -8\/5.\u00a0 Again, check the value of x, so that x \u2013 (2)(-8\/5) =8, or\u00a0\u00a0\u00a0\u00a0 \u00a0x +16\/5 =8.\u00a0 (Notice how the sign changes when two negative values are multiplied.) Then multiply both sides by 5, so that 5x +16 = 40, or 5x =24 or x = 24\/5.\u00a0 To check the first equation, 24\/5 \u2013 2[-8\/5] equals 24\/5 +16\/5 = 40\/5, or 8.\u00a0 To check the second equation 2 (24\/5) \u2013 (8\/5) = 48\/5 \u2013 8\/5) = 40\/5 = 8.<\/p>\n

 <\/p>\n

<\/h4>\n

Understanding the Problem and Developing a Plan<\/strong><\/h4>\n

Math problems that are written in words can often be translated into systems of equations, then solved by using substitution.\u00a0 Suppose the statement were \u201cThe sum of two numbers is 82.\u00a0 One number is 12 more than the other.\u00a0 What is the larger number?\u201d\u00a0 The first sentence can be represented by the equation x +y = 82.\u00a0 The second sentence can be represented by the equation x=12 +y.<\/p>\n

Problem-Solving:\u00a0 Solving the Problem and Checking the Answer<\/strong><\/h4>\n

To solve the problem, take the system of equations and use substitution, so that 12 +y +y = 82, then 2y = 82-12, or 2y = 70, then y = 70\/2, or 35. \u00a0Using the second equation to solve for x, 12 +35 = 47, and using the first equation, 47 +35 = 82.<\/p>\n

<\/h4>\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 Columbia, SC: visit:\u00a0 Tutoring in Columbia, SC<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview One of the ways to solve systems of equations is by graphing the equations.\u00a0 However, graphing the equations is not always the most accurate method to solve them.\u00a0 If one variable in a system is represented in terms of the other variable in the system, the systems can be solved by substitution. Using Substitution […]<\/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":[3731,3289,1752],"class_list":["post-9076","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-problem-solving-in-math","tag-solving-systems-of-equations","tag-substitution"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9076","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=9076"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9076\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=9076"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=9076"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=9076"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}