{"id":3291,"date":"2023-10-04T13:58:28","date_gmt":"2023-10-04T13:58:28","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=3291"},"modified":"2023-10-04T14:01:39","modified_gmt":"2023-10-04T14:01:39","slug":"week-4-ss2-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-ss2-second-term-mathematics-notes\/","title":{"rendered":"Week 4 – SS2 Second Term Mathematics Notes"},"content":{"rendered":"

WEEK FOUR
\n<\/strong>SOLUTIONS OF INEQUALITIES OF TWO VARIABLES AND THE RANGE OF VALUES OF COMBINED INEQUALITIES
\n<\/strong>A linear inequality in two variables x and y is of the form: ax + by c: ax + by < c: ax + by > c ax + by c where a, b and c are constants. A solution to an inequality is any pair of number x and y that satisfies the inequality.
\nExample 2
\n<\/strong>Determine the solution set of 5x + 2y 17
\nSolution
\n<\/strong>One solution to 5x + 2y < 17 is x =2 and y = 3 because 5(2) + 2(3) = 16, which is indeed less than 17. But the pair x = 2 and y = 3 is not the only solution. As a matter of fact, there are infinitely many solutions. If the pairs of numbers x and y is a solution, then think of this pair as a point in the plane, so the set of all solutions can be thought of as a REGION in the x \u2013y plane.
\nHence, to illustrate how to determine this region, first express y in terms of x in the inequality.
\n3x + 2y 17
\n2y -5x + 17
\nY +
\nWhen x = 0, y = 8.5; when y = 0, x = 3 (show in a graph)
\nThe shaded Region is the solution set.<\/p>\n

\u00a0
\n\u00a0
\n\u00a0\"\"\/\"\"\/RANGE OF VALUES OF COMBINED INEQUALITIES
\n<\/strong>\"\"\/\"\"\/\"\"\/
\n\t\t\t<\/strong>\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/
\n\t\t\t<\/strong>In the above diagram, x can possess any value between -4 and +3 inclusive Hence x -2 and x + 3 or -4 x and x +3
\nThese two inequalities can be combined as a single inequality. Thus, -4 x + 3
\nExample 3
\n<\/strong>What is the range of values of x for which 2x + 6 > 2 and x \u2013 4 < 1 are both satisfied?
\nSolution
\n2x + 6 > 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x \u2013 4 < 1
\n2x > 2 \u2013 6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x < 1 + 4
\n2x > – 6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0x < 5
\nX > -2
\n\"\"\/Hence x > – 2 and x < 5 or -2 < x and x < 5 or -2 < x < 5. Both inequalities are satisfied if -2 < x and x < 5 or -2 < x < 5
\n\"\"\/\"\"\/\"\"\/\"\"\/a)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0b)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0c)\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0WRAP UP AND ASSESSMETNS
\n<\/strong>AN Inequality is any statement involving one of symbols <, >, and. Simple linear inequalities can be represented on a number line.
\nTicket out ;<\/strong>Pg 207 Exercise 15.1 no 2d, f & No 8
\n
\n\t\t\t<\/strong>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

WEEK FOUR SOLUTIONS OF INEQUALITIES OF TWO VARIABLES AND THE RANGE OF VALUES OF COMBINED…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,264],"tags":[],"class_list":["post-3291","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss2-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3291","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=3291"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3291\/revisions"}],"predecessor-version":[{"id":3292,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3291\/revisions\/3292"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=3291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=3291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=3291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}