{"id":2471,"date":"2012-07-19T20:11:57","date_gmt":"2012-07-19T20:11:57","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=2471"},"modified":"2014-12-02T08:32:08","modified_gmt":"2014-12-02T08:32:08","slug":"number-theory-linear-equations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/number-theory-linear-equations\/","title":{"rendered":"Number Theory: Linear Equations"},"content":{"rendered":"

A linear equation is an equation<\/a> whose degree is 1<\/strong>. i.e. In a linear equation, the highest power of the variable is 1<\/strong>.<\/p>\n

Example:<\/span><\/strong><\/p>\n

i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x+3 = 5<\/strong><\/p>\n

ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 y-5=8<\/strong><\/p>\n

Solution (or) Root of a Linear Equation:<\/h4>\n

A value or a number which satisfies the given linear equation is called its root or solution.<\/p>\n

Example:<\/span><\/strong><\/p>\n

i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2<\/strong> is the solution of x+3=5<\/strong> because 2+3=5<\/strong>.<\/p>\n

ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 13<\/strong> is the solution of y-5=8<\/strong> because 13-5=8<\/strong>.<\/p>\n

Solving a Linear Equation:<\/h4>\n

A linear equation may involve the operations addition, subtraction, multiplication or division and the following steps are to be followed for the respective operations.<\/p>\n

i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 When the variable in a linear equation is getting added<\/strong> to a number, the same is subtracted<\/strong> from the equation to obtain the solution.<\/p>\n

Example:<\/span><\/strong><\/p>\n

x + 5 = 8<\/strong><\/p>\n

Subtracting 5<\/strong> from both sides,<\/p>\n

X = 8-5 = 3<\/strong>.<\/p>\n

ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 When some number is getting subtracted<\/strong> from the variable in a linear equation, the same number is added <\/strong>to the equation to obtain the solution.<\/p>\n

Example:<\/span><\/strong><\/p>\n

x-5 = 8<\/strong><\/p>\n

Adding 5 both sides,<\/p>\n

x = 8+5 = 13<\/strong><\/p>\n

iii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0When the variable in a linear equation is getting multiplied<\/strong> by a number, the equation is divided<\/strong> by the same number to obtain the solution.<\/p>\n

Example:<\/span><\/strong><\/p>\n

5x = 20<\/strong><\/p>\n

Dividing both sides by 5<\/strong>,<\/p>\n

x= 20\/5 = 4.<\/strong><\/p>\n

iv)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 When the variable in a linear equation is getting divided <\/strong>by a number, the equation is multiplied<\/strong> by the same number to obtain the solution.<\/p>\n

Example:<\/span><\/strong><\/p>\n

x\/5 = 4<\/strong><\/p>\n

multiplying both sides by 5<\/strong>,<\/p>\n

x = 4×5 = 20.<\/strong><\/p>\n

 <\/p>\n

SchoolTutoring Academy 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 Oceanside visit: Tutoring in Oceanside. <\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

A linear equation is an equation whose degree is 1. i.e. In a linear equation, the highest power of the variable is 1. Example: i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x+3 = 5 ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 y-5=8 Solution (or) Root of a Linear Equation: A value or a number which satisfies the given linear equation is called its root or solution. Example: […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,11],"tags":[588,1045,1558,1682,1688],"class_list":["post-2471","post","type-post","status-publish","format-standard","hentry","category-algebra","category-math-fundamentals","tag-equation","tag-linear","tag-root","tag-solution","tag-solving"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2471","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=2471"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2471\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=2471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=2471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=2471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}