{"id":1547,"date":"2023-09-29T10:18:49","date_gmt":"2023-09-29T10:18:49","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=1547"},"modified":"2023-09-29T10:22:50","modified_gmt":"2023-09-29T10:22:50","slug":"week-3-and-4-jss-3-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-3-and-4-jss-3-second-term-mathematics-notes\/","title":{"rendered":"Week 3 and 4 – Jss 3 Second Term Mathematics Notes"},"content":{"rendered":"

WEEK 3
\n<\/strong> ELIMINATION METHOD
\n<\/strong>This method is very useful to solve simultaneous equations especially when none of the coefficients of the unknown is 1.
\nExample III.
\nSolve the following simultaneous equations by elimination method.
\n(a)\u00a0\u00a0\u00a0\u00a06x + 5y = 15\u00a0\u00a0\u00a0\u00a0(1)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(b)\u00a0\u00a0\u00a0\u00a04c \u2013 4d = 9
\n\u00a0\u00a0\u00a0\u00a03x + 5y = 12\u00a0\u00a0\u00a0\u00a0(2)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a05c + 4d = 18
\nOne of the unknown “Y” has equal coefficient and with the same signs so we subtract the two equations to eliminate y terms.
\n6x + 5y \u2013 (3x + 5y) = 15 – 12
\n6x + 5y – 3x – 5y = 3
\n6x – 3x + 5y – 5y = 3
\n3x + 0 = 3
\n=
\nx=1<\/p>\n

\u00a0To find y, substitute x=1 in either (1) or (2) using equation
\n (1) 6x + 5y = 15
\n6(i) + 5y = 15
\n6 + 5y = 15
\n5y = 15 \u2013 6
\n =
\ny=
\n(b)\u00a0\u00a0\u00a0\u00a04c \u2013 4d = 9 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(1)
\n\u00a0\u00a0\u00a0\u00a05c + 4d = 18 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(2)
\nOne of the unknown “d” has equal coefficient but with different sign so we add the two equations to eliminate “d”
\n4c \u2013 4d + 5c + 4d = 9 + 18
\n4c + 5c \u2013 4d + 4d = 27
\n =
\nC = 3
\nTo find d substitute c = 3 into (1)
\n4c \u2013 4d = 9
\n4(3) \u2013 4d = 9
\n4d = 12 – 9
\n=
\nD =
\nWRAP UP AND ASSESSMENT
\n<\/strong>In elimination method you may need to multiply one or both of the equations by a number in order to obtain a variable with e same coefficient in both equations. Then add both equations when the signs of the variables you want to eliminate are opposite but subtract them when the signs are the same.
\nExercise: 16 4 No 2, 3, 7 \u2013 11.
\nUse elimination method to solve the following simultaneous equations.
\n2.\u00a0\u00a0\u00a0\u00a06x + 7y = 15\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04x + 3y = 10
\n\u00a0\u00a0\u00a0\u00a06x \u2013 9y = 31\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04x + 5y = 8<\/p>\n

\u00a07)\u00a0\u00a0\u00a0\u00a02x + 3y = 8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a08)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03x + 4y = 10
\n\u00a0\u00a0\u00a0\u00a03x + 2y = 7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a02x + 5y = 9<\/p>\n

\u00a09)\u00a0\u00a0\u00a0\u00a04x + 3y = 11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04a + 3b = 3
\n\u00a0\u00a0\u00a0\u00a03x \u2013 4y = 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a03a + 2b = 1<\/p>\n

\u00a0TICKET OUT
\n<\/strong>Solve the following Simultaneous equation by Elimination method. Exercise 16.4 No 12 -1<\/p>\n

\u00a0
\n\u00a0 WEEK 4
\n<\/strong>SOLVING SIMULTANEOUS EQUATION GRAPHICALLY
\n<\/strong>To solve simultaneous equations graphically.<\/p>\n

    \n
  1. \n
    Make a table of values for both equations.\n<\/div>\n<\/li>\n
  2. \n
    Draw the graphs for both equations on the same axes\n<\/div>\n<\/li>\n
  3. \n
    Find the co-ordinate (i.e x and y values) where both graphs intersect these values are the solutions of both equations.\n<\/div>\n<\/li>\n
  4. \n
    Check your solutions by putting these values into the original equations to make sure they satisfy them.\n<\/div>\n<\/li>\n<\/ol>\n

    Example 16.3
    \nSolve the simultaneous equations.
    \nX \u2013 2y = 4 and 2x \u2013 y = 5 graphically
    \nSolution
    \nIn each equation make y the subject of the equation
    \n(i)\u00a0\u00a0\u00a0\u00a0 x \u2013 2y = 4
    \n\u00a0\u00a0\u00a0\u00a0-2y = 4 \u2013 x
    \n\u00a0\u00a0\u00a0\u00a0 y = -2 + 0.5x \u2026\u2026\u2026\u2026\u2026\u2026 (1)<\/p>\n

    \u00a0
    \n\t\t\t<\/strong>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

    WEEK 3 ELIMINATION METHOD This method is very useful to solve simultaneous equations especially when…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,142],"tags":[],"class_list":["post-1547","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-jss3-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1547","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=1547"}],"version-history":[{"count":2,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1547\/revisions"}],"predecessor-version":[{"id":1549,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1547\/revisions\/1549"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=1547"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=1547"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=1547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}