{"id":18303,"date":"2016-10-15T15:08:05","date_gmt":"2016-10-15T15:08:05","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=18303"},"modified":"2016-10-15T15:08:05","modified_gmt":"2016-10-15T15:08:05","slug":"algebra-how-to-solve-a-system-of-three-equations-by-hand","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/algebra-how-to-solve-a-system-of-three-equations-by-hand\/","title":{"rendered":"Algebra: how to solve a system of three equations by hand"},"content":{"rendered":"

The tutor shows an example of solving a three-variable linear system algebraically.<\/h1>\n

Example: Solve the following system of equations:<\/strong><\/p>\n

    \n
  1. -3x + 2y + z = 16<\/li>\n
  2. x – y – 3z =-19<\/li>\n
  3. 2x + y + 7z = 30<\/li>\n

    The first idea is to eliminate the same variable in two ways, leaving a system of two equations in two variables.
    \nWe might add the first with twice the second:
    \n-3x + 2y + z = 16
    \n 2x – 2y – 6z =-38<\/span><\/p>\n

  4. -x -5z = -22<\/li>\n

    Similarly, we can add the second to the third:
    \n x – y – 3z =-19
    \n 2x + y + 7z = 30<\/span><\/p>\n

  5. 3x + 4z = 11<\/li>\n

    Next, we can eliminate x by adding 3(IV) to V:
    \n -3x – 15z = -66
    \n 3x + 4z = 11<\/u>
    \n – 11z = -55<\/p>\n

    Therefore, z=5.<\/p>\n

    We can substitute z=5 back into V, for instance, to get x:<\/p>\n

    3x + 4(5) = 11 ⇒ 3x + 20 = 11 ⇒ 3x = -9 ⇒x = -3<\/p>\n

    Now, subbing both x=-3 and z=5 into III we get<\/p>\n

    2(-3) + y +7(5) = 30 ⇒ y = 1<\/p>\n

    Apparently the solution is<\/p>\n

    x=-3, y=1, z=5<\/p>\n

    HTH:)<\/p>\n

    Source:<\/p>\n

    Travers, Kenneth et al. Using Advanced Algebra<\/u>. Toronto: Doubleday Canada, 1977.<\/p>\n

    Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

    The tutor shows an example of solving a three-variable linear system algebraically. Example: Solve the following system of equations: -3x + 2y + z = 16 x – y – 3z =-19 2x + y + 7z = 30 The …<\/p>\n

    Algebra: how to solve a system of three equations by hand<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1970],"class_list":["post-18303","post","type-post","status-publish","format-standard","hentry","category-math","tag-how-to-solve-a-system-of-three-equations-algebraically"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18303","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=18303"}],"version-history":[{"count":40,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18303\/revisions"}],"predecessor-version":[{"id":18344,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18303\/revisions\/18344"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=18303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=18303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=18303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}