{"id":46124,"date":"2025-07-01T19:29:19","date_gmt":"2025-07-01T19:29:19","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=46124"},"modified":"2025-07-01T19:29:20","modified_gmt":"2025-07-01T19:29:20","slug":"does-the-system-have-one-none-or-infinite-solutions","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/does-the-system-have-one-none-or-infinite-solutions\/","title":{"rendered":"Does the system have one, none or infinite solutions"},"content":{"rendered":"\n

Does the system have one, none or infinite solutions? 8x + 4y = 12 y = -2x + 3<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

We are given the system of equations:<\/p>\n\n\n\n

    \n
  1. 8x+4y=128x + 4y = 128x+4y=12<\/li>\n\n\n\n
  2. y=\u22122x+3y = -2x + 3y=\u22122x+3<\/li>\n<\/ol>\n\n\n\n

    To determine if the system has one solution, no solution, or infinite solutions, we can solve the system by substitution or elimination. Let’s use substitution, since the second equation already expresses yyy in terms of xxx.<\/p>\n\n\n\n

    Step 1: Substitute the expression for yyy from the second equation into the first equation.<\/h3>\n\n\n\n

    We know from the second equation that y=\u22122x+3y = -2x + 3y=\u22122x+3. Now, substitute this into the first equation:8x+4(\u22122x+3)=128x + 4(-2x + 3) = 128x+4(\u22122x+3)=12<\/p>\n\n\n\n

    Step 2: Simplify the equation.<\/h3>\n\n\n\n

    Distribute the 4 on the left-hand side:8x\u22128x+12=128x – 8x + 12 = 128x\u22128x+12=12<\/p>\n\n\n\n

    This simplifies to:0x+12=120x + 12 = 120x+12=12<\/p>\n\n\n\n

    Which is equivalent to:12=1212 = 1212=12<\/p>\n\n\n\n

    Step 3: Interpret the result.<\/h3>\n\n\n\n

    Since this is a true statement and doesn’t involve xxx, it means the equation is satisfied for any value of xxx. Therefore, the system has infinite solutions<\/strong>. This happens because the two equations represent the same line, so every point on the line is a solution.<\/p>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n

    The system has infinite solutions<\/strong> because the two equations are equivalent, meaning they represent the same line on the coordinate plane. Every point on this line satisfies both equations.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Does the system have one, none or infinite solutions? 8x + 4y = 12 y = -2x + 3 The Correct Answer and Explanation is: We are given the system of equations: To determine if the system has one solution, no solution, or infinite solutions, we can solve the system by substitution or elimination. Let’s […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-46124","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46124","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=46124"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46124\/revisions"}],"predecessor-version":[{"id":46126,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46124\/revisions\/46126"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=46124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=46124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=46124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}