{"id":42806,"date":"2025-06-29T10:28:56","date_gmt":"2025-06-29T10:28:56","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42806"},"modified":"2025-06-29T10:28:58","modified_gmt":"2025-06-29T10:28:58","slug":"solve-the-following-system-of-equations-for-x-and-y-by-cross-multiplication-11x-5y-7-0-and-6x-3y-21-0","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/solve-the-following-system-of-equations-for-x-and-y-by-cross-multiplication-11x-5y-7-0-and-6x-3y-21-0\/","title":{"rendered":"Solve the following system of equations for x and y by cross multiplication: 11x + 5y – 7 = 0 and 6x – 3y – 21 = 0."},"content":{"rendered":"\n

Solve the following system of equations for x and y by cross multiplication: 11x + 5y – 7 = 0 and 6x – 3y – 21 = 0.<\/p>\n\n\n\n

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

To solve the system of equations by cross-multiplication, we start with the following system:<\/p>\n\n\n\n

    \n
  1. 11x+5y\u22127=011x + 5y – 7 = 011x+5y\u22127=0<\/li>\n\n\n\n
  2. 6x\u22123y\u221221=06x – 3y – 21 = 06x\u22123y\u221221=0<\/li>\n<\/ol>\n\n\n\n

    Step 1: Rearranging the equations<\/h3>\n\n\n\n

    First, we rewrite both equations in a form that is suitable for cross-multiplication. This means isolating the constants on one side.<\/p>\n\n\n\n

    For the first equation: 11x+5y\u22127=0\u2005\u200a\u27f9\u2005\u200a11x+5y=7(Equation 1)11x + 5y – 7 = 0 \\implies 11x + 5y = 7 \\quad \\text{(Equation 1)}11x+5y\u22127=0\u27f911x+5y=7(Equation 1)<\/p>\n\n\n\n

    For the second equation: 6x\u22123y\u221221=0\u2005\u200a\u27f9\u2005\u200a6x\u22123y=21(Equation 2)6x – 3y – 21 = 0 \\implies 6x – 3y = 21 \\quad \\text{(Equation 2)}6x\u22123y\u221221=0\u27f96x\u22123y=21(Equation 2)<\/p>\n\n\n\n

    Now, we have the system: 11x+5y=711x + 5y = 711x+5y=7 6x\u22123y=216x – 3y = 216x\u22123y=21<\/p>\n\n\n\n

    Step 2: Cross-multiplication method<\/h3>\n\n\n\n

    The method of cross-multiplication can be applied by treating this system as if it were two fractions. We first write both equations in the form of fractions: x7=y\u22123=z21\\frac{x}{7} = \\frac{y}{-3} = \\frac{z}{21}7x\u200b=\u22123y\u200b=21z\u200b<\/p>\n\n\n\n

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

    Solve the following system of equations for x and y by cross multiplication: 11x + 5y – 7 = 0 and 6x – 3y – 21 = 0. The Correct Answer and Explanation is: To solve the system of equations by cross-multiplication, we start with the following system: Step 1: Rearranging the equations First, we […]<\/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-42806","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42806","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=42806"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42806\/revisions"}],"predecessor-version":[{"id":42808,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42806\/revisions\/42808"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}