3w – 4z = 8 2w + 3z = -6 solve<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n We are given a system of two linear equations:<\/p>\n\n\n\n We want to eliminate one variable by making the coefficients of either ww or zz the same (or opposites). Let’s eliminate zz. Multiply equation (1) by 3<\/strong>: 3(3w\u22124z)=3(8)\u21d29w\u221212z=24(3)3(3w – 4z) = 3(8) \\Rightarrow 9w – 12z = 24 \\tag{3}<\/p>\n\n\n\n Multiply equation (2) by 4<\/strong>: 4(2w+3z)=4(\u22126)\u21d28w+12z=\u221224(4)4(2w + 3z) = 4(-6) \\Rightarrow 8w + 12z = -24 \\tag{4}<\/p>\n\n\n\n (9w\u221212z)+(8w+12z)=24+(\u221224)(9w – 12z) + (8w + 12z) = 24 + (-24)<\/p>\n\n\n\n Simplify: 17w=0\u21d2w=017w = 0 \\Rightarrow w = 0<\/p>\n\n\n\n Use equation (1): 3w\u22124z=8\u21d23(0)\u22124z=8\u21d2\u22124z=8\u21d2z=\u221223w – 4z = 8 \\Rightarrow 3(0) – 4z = 8 \\Rightarrow -4z = 8 \\Rightarrow z = -2<\/p>\n\n\n\n w=0,z=\u22122\\boxed{w = 0, \\quad z = -2}<\/p>\n\n\n\n This problem involves solving a system of linear equations with two variables using the elimination method<\/strong>, a strategy to remove one variable so we can solve for the other.<\/p>\n\n\n\n We started with:<\/p>\n\n\n\n To eliminate one variable, we decided to eliminate zz. The goal was to manipulate the equations so the coefficients of zz become opposites. The least common multiple (LCM) of 4 and 3 is 12, so we multiplied the equations to get \u221212z-12z and +12z+12z. Specifically:<\/p>\n\n\n\n Adding these two new equations cancels the zz terms, leaving a single-variable equation: 9w+8w=17w=0\u21d2w=09w + 8w = 17w = 0 \\Rightarrow w = 0<\/p>\n\n\n\n Substituting w=0w = 0 back into the original equation allows us to solve for zz: 3(0)\u22124z=8\u21d2z=\u221223(0) – 4z = 8 \\Rightarrow z = -2<\/p>\n\n\n\n This solution means the values w=0w = 0 and z=\u22122z = -2 satisfy both<\/strong> original equations, making it the unique solution<\/strong> to the system. Solving systems like this is important in algebra and real-world applications such as economics, physics, and engineering, where multiple conditions must be satisfied simultaneously.<\/p>\n","protected":false},"excerpt":{"rendered":" 3w – 4z = 8 2w + 3z = -6 solve The correct answer and explanation is: We are given a system of two linear equations: Step 1: Use the method of elimination to eliminate one variable. We want to eliminate one variable by making the coefficients of either ww or zz the same (or […]<\/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-22599","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22599","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=22599"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22599\/revisions"}],"predecessor-version":[{"id":22601,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22599\/revisions\/22601"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Use the method of elimination<\/strong> to eliminate one variable.<\/h3>\n\n\n\n
To do this, find the least common multiple (LCM) of the coefficients of zz:<\/p>\n\n\n\n\n
We\u2019ll multiply each equation to get zz terms to be opposites:<\/li>\n<\/ul>\n\n\n\nStep 2: Add equations (3) and (4) to eliminate zz:<\/h3>\n\n\n\n
Step 3: Substitute w=0w = 0 into one of the original equations to find zz:<\/h3>\n\n\n\n
\u2705 Final Answer:<\/h3>\n\n\n\n
\n\n\n\n\u270d\ufe0f 300-Word Explanation:<\/h3>\n\n\n\n
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