{"id":9114,"date":"2017-03-23T04:09:20","date_gmt":"2017-03-23T04:09:20","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=9114"},"modified":"2017-03-23T04:09:20","modified_gmt":"2017-03-23T04:09:20","slug":"math-review-of-problem-solving-with-systems-of-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2017\/03\/23\/math-review-of-problem-solving-with-systems-of-equations\/","title":{"rendered":"Math Review of Problem Solving with Systems of Equations"},"content":{"rendered":"

Overview<\/strong><\/h3>\n

Systems of two equations with two variables can also be used to solve problems.\u00a0 In order to solve the problem, it can be translated to a system of equations.\u00a0 Once the problem is understood, students can make a plan, find the answer, and check to make sure it is correct.<\/p>\n

Understand the Problem<\/strong><\/h3>\n

In order to understand the word problem, read it very carefully and note the questions asked, the data given.\u00a0 Pay attention to any word cues that indicate mathematical relationships.\u00a0 Suppose a basketball team played 180 games and they won 40 more games than they lost.\u00a0 How many games did the team lose?\u00a0 In that case, the team played 180 games total.\u00a0 40 more games were won than lost.<\/p>\n

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Make a Plan<\/strong><\/h3>\n

In making a plan, write a system of equations to fit the problem.\u00a0 Let x be the number of games won and y be the number of games lost.\u00a0 In the first equation, x +y = 180.\u00a0 In the second equation, x \u2013y =40.\u00a0 Those equations can be combined to find the answer.<\/p>\n

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Find the Answer<\/strong><\/h3>\n

This system of equations can be solved by the addition method, as x +y = 180 and x-y = 40.\u00a0 Therefore 2x +(y-y) = 180 +40, or 2x= 220.\u00a0 Solving for x, divide both sides by 2, so x =110.\u00a0 Solving for y, 180 -110 = 70.<\/p>\n

Check the Work<\/strong><\/h3>\n

To see if both sentences are true, 110 +70 equals 180, and 110-70 equals 40. The same sort of process can be used to solve equations by choosing the substitution method.\u00a0 Suppose that Matilde is 13 years older than Ana.\u00a0 In 9 years, Matilde will be twice as old as Ana.\u00a0 Let x be Matilde\u2019s age and y be Ana\u2019s age.\u00a0 There are two equations in the plan, x =y +13, and x +9 =2(y +9).\u00a0 \u00a0Using substitution, x = y + 13, and x = 2y +9, so y +13 =2y +9, so y = 13-9, or 4.\u00a0 Ana is 4, and Matilde is 17.\u00a0 In 9 years Matilde will be 26, and Ana will be 4+9 or 13. Matilde is twice Ana\u2019s age in 9 years, and the answers check.<\/p>\n

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SchoolTutoring Academy<\/a>\u00a0<\/span><\/strong>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 Farmville, VA: visit:\u00a0 Tutoring in Farmville, VA<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Systems of two equations with two variables can also be used to solve problems.\u00a0 In order to solve the problem, it can be translated to a system of equations.\u00a0 Once the problem is understood, students can make a plan, find the answer, and check to make sure it is correct. Understand the Problem In […]<\/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":[3289,2582],"class_list":["post-9114","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-solving-systems-of-equations","tag-word-problems"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9114","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=9114"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/9114\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=9114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=9114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=9114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}