[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522774-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522774-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","solving-systems-of-three-equations-w-cramers-rule-systems-of-three-equations-worksheet","Solving Systems of Three Equations w/ Cramer's Rule - Systems of Three Equations - Worksheet","","Worksheet-style practice for solving multiple linear systems of three equations using Cramer’s Rule. Each problem provides three-variable equations in x, y, and z, with some systems designed to yield a single ordered triple solution. Several items illustrate special cases such as no solution and infinitely many solutions. Guided by substitution of determinants and equation manipulation, the set supports step-by-step computation and answer verification for typical Algebra 2 curriculum practice.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/solving-systems-of-three-equations-w-cramers-rule-systems-of-three-equations-worksheet/522774/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/solving-systems-of-three-equations-w-cramers-rule-systems-of-three-equations-worksheet/522774.png","ImageObject",300,407,{"name":42,"@type":43},"Sophia Brooks","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",8,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What method does the worksheet require to solve each system?","Question",{"text":63,"@type":64},"It instructs using Cramer’s Rule to solve each system of three equations.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are the answers presented in the worksheet?",{"text":68,"@type":64},"Some systems include an ordered triple solution (x, y, z). Other systems are labeled as “No solution” or “Infinitely many solutions.”",{"name":70,"@type":61,"acceptedAnswer":71},"What variables are used in the systems?",{"text":72,"@type":64},"The equations are in three variables: x, y, and z.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522774,1791504837,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":123,"preview_page_count":4},962084925636,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Kuta Software-Infinite Algebra 2 Name   \nSolving Systems of Three Equations w/ Cramer's Rule Date  Period   \nUse Cramer's Rule to solve each system.  \n1) −2x − 5 y + 4z = 21 2) 5x + y − 4z = −4  \n−5x − 5 y + z = 21 −3 y − 6z = −21  \n−4 y − 4z = 8 − x − y − z = −6  \n3) −4x − 6z = −12 4) 4x − 4 y + 2z = −14  \n−6x − 4 y − 2z = 6 4x + 2y = 14  \n− x + 2y + z = 9 −3 y + z = −10  \n5) x − 3 y + z = −7 6) 6x + 3y − 3z = −18  \n−4x − 6z = 4 6x + y + 4z = −28  \n2x + 3y + 2z = 4 5z = −10  \n7) −12x − 4 y + 4z = −21 8) 4x + 5y = −6  \n−4z = 6 10x − 30 y + 50z = −27  \n12x + 12 y + 4z = −1 4x + 4y + z = −6  \n9) 36x − 6 y + 6z = −1 10) −2x + y − 4z = 4  \n12x + 6z = −3 5x − 2 y = 18  \n18x − 6 y + 6z = −1 x − 5z = 17  \n11) −3z = 6 12) 6 y + 6z = −30  \n2x + y − 2z = 6 4x − 6 y − 3z = 26  \n−6x − 3 y = −6 x + y + z = −3  \n13) −6x − y + z = −7 14) 3x + 6y = −4  \n4z = −6 x + y − z = −2  \n4x − 24 y + 24z = 17 9x − 12 y + 15z = 28  \n15) 5x + 5y + 30z = 24 16) 3x − 1 = 3z  \n5x − 5 y − 20z = −11 4 = 6y − 3z − 3x  \n−4 y + 10z = 1 −2x + 6z = 10 y − 7  \nKuta Software-Infinite Algebra 2 Name   \nSolving Systems of Three Equations w/ Cramer's Rule Date  Period   \nUse Cramer's Rule to solve each system.  \n1) −2x − 5 y + 4z = 21  \n−5x − 5 y + z = 21  \n−4 y − 4z = 8  \n(−1, −3, 1)  \n3) −4x − 6z = −12  \n−6x − 4 y − 2z = 6  \n− x + 2y + z = 9  \n(−3, 1, 4)  \n5) x − 3 y + z = −7  \n−4x − 6z = 4  \n2x + 3y + 2z = 4  \n(−1, 2, 0)  \n7) −12x − 4 y + 4z = −21  \n−4z = 6  \n12x + 12 y + 4z = −1  \n(~~ ~~53~~ ~~ , − ~~ ~~54~~ ~~ , − ~~ ~~32)  \n2) 5x + y − 4z = −4  \n−3 y − 6z = −21  \n− x − y − z = −6  \n(5, −5, 6)  \n4) 4x − 4 y + 2z = −14  \n4x + 2y = 14  \n−3 y + z = −10  \nNo solution  \n6) 6x + 3y − 3z = −18  \n6x + y + 4z = −28  \n5z = −10  \n(−3, −2, −2)  \n8) 4x + 5y = −6  \n10x − 30 y + 50z = −27  \n4x + 4y + z = −6  \n(~~ ~~12~~ ~~ , − ~~ ~~85~~ ~~ , − ~~ ~~85)  \n9) 36x − 6 y + 6z = −1  \n12x + 6z = −3  \n18x − 6 y + 6z = −1  \n(0, − ~~ ~~13~~ ~~ , − ~~ ~~12)  \n11) −3z = 6  \n2x + y − 2z = 6  \n−6x − 3 y = −6  \nInfinitely many solutions  \n13) −6x − y + z = −7  \n4z = −6  \n4x − 24 y + 24z = 17  \n(~~ ~~54~~ ~~ , −2, − ~~ ~~32)  \n15) 5x + 5y + 30z = 24  \n5x − 5 y − 20z = −11  \n−4 y + 10z = 1  \n(~~ ~~45~~ ~~ , 1, ~~ ~~12~~ ~~ )  \n10) −2x + y − 4z = 4  \n5x − 2 y = 18 x − 5z = 17  \n(2, −4, −3)  \n12) 6 y + 6z = −30  \n4x − 6 y − 3z = 26 x + y + z = −3  \n(2, −1, −4)  \n14) 3x + 6y = −4 x + y − z = −2  \n9x − 12 y + 15z = 28  \n(0, − ~~ ~~23~~ ~~ , 43)  \n16) 3x − 1 = 3z  \n4 = 6y − 3z − 3x  \n−2x + 6z = 10 y − 7  \n(0, ~~ ~~12~~ ~~ , − ~~ ~~13)  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaidIiHjFwZZMh","https://ap.wps.com/l/cbCaidIiHjFwZZMh","pdf",33200,"English","# Use Cramer's Rule to Solve Each System\n## Problems 1-16 with x, y, z systems\n## Solution types: unique, no solution, infinitely many solutions","[{\"question\":\"What method does the worksheet require to solve each system?\",\"answer\":\"It instructs using Cramer’s Rule to solve each system of three equations.\"},{\"question\":\"How are the answers presented in the worksheet?\",\"answer\":\"Some systems include an ordered triple solution (x, y, z). Other systems are labeled as “No solution” or “Infinitely many solutions.”\"},{\"question\":\"What variables are used in the systems?\",\"answer\":\"The equations are in three variables: x, y, and z.\"}]","Solving Systems of Three Equations w/ Cramer's Rule - Systems of Three Equations - Worksheet | PDF",1791426157]