[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-522777-en":59,"doc-seo-522777-105":80},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":72,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":52,"preview_page_count":4},522777,962084925636,"Sophia Brooks","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","Solving Systems of Three Equations w/ Elimination - Worksheet","Algebra 2 elimination worksheets focused on solving systems of three linear equations. Each problem instructs students to use elimination to find the triple solution (x, y, z) when it exists, and to identify cases with no unique solution when the system is dependent or inconsistent. A set of numbered systems (1–16) is provided, followed by a critical thinking task requiring constructing a system that matches a specified solution (2, 1, 0).","Kuta Software-Infinite Algebra 2 Name___________________________________  \nSolving Systems of Three Equations w/ Elimination Date________________ Period____  \nSolve each system by elimination.  \n1) −x − 5 y − 5z = 2 2) −4x − 5 y − z = 18  \n4x − 5 y + 4z = 19 −2x − 5 y − 2z = 12 x + 5 y − z = −20 −2x + 5 y + 2z = 4  \n3) −x − 5 y + z = 17 4) 4x + 4 y + z = 24  \n−5x − 5 y + 5z = 5 2x − 4 y + z = 0  \n2x + 5 y − 3z = −10 5x − 4 y − 5z = 12  \n5) 4r − 4s + 4t = −4 6) x − 6 y + 4z = −12  \n4r + s − 2t = 5 x + y − 4z = 12  \n−3r − 3s − 4t = −16 2x + 2 y + 5z = −15  \n7) x − y − 2z = −6 8) 5a + 5b + 5c = −20  \n3x + 2 y = −25 4a + 3b + 3c = −6  \n−4x + y − z = 12 −4a + 3b + 3c = 9  \n9) −6r + 5s + 2t = −11 10) −6x − 2 y + 2z = −8  \n−2r + s + 4t = −9 3x − 2 y − 4z = 8  \n4r − 5s + 5t = −4 6x − 2 y − 6z = −18  \n11) 5x − 4 y + 2z = 21 12) 6r − s + 3t = −9  \n−x − 5 y + 6z = −24 5r + 5s − 5t = 20  \n−x − 4 y + 5z = −21 3r − s + 4t = −5  \n13) −3a − b − 3c = −8 14) −5x + 3 y + 6z = 4  \n−5a + 3b + 6c = −4 −3x + y + 5z = −5  \n−6a − 4b + c = −20 −4x + 2 y + z = 13  \n15) 3a − 3b + 4c = −23 16) −6x − 2 y − z = −17 a + 2b − 3c = 25 5x + y − 6z = 19  \n4a − b + c = 25 −4x − 6 y − 6z = −20  \nCritical thinking question:  \n17) Write a system of equations with the solution (2, 1, 0) .  \nKuta Software-Infinite Algebra 2 Name   \nSolving Systems of Three Equations w/ Elimination Date  Period   \nSolve each system by elimination.  \n1) −x − 5 y − 5z = 2  \n4x − 5 y + 4z = 19 x + 5 y − z = −20  \n(−2, −3, 3)  \n3) −x − 5 y + z = 17  \n−5x − 5 y + 5z = 5  \n2x + 5 y − 3z = −10  \n(−1, −4, −4)  \n5) 4r − 4s + 4t = −4  \n4r + s − 2t = 5  \n−3r − 3s − 4t = −16  \n( 1, 3, 1)  \n7) x − y − 2z = −6  \n3x + 2 y = −25  \n−4x + y − z = 12  \n(−5, −5, 3)  \n2) −4x − 5 y − z = 18  \n−2x − 5 y − 2z = 12  \n−2x + 5 y + 2z = 4  \n(−4, 0, −2)  \n4) 4x + 4 y + z = 24  \n2x − 4 y + z = 0  \n5x − 4 y − 5z = 12  \n(4, 2, 0)  \n6) x − 6 y + 4z = −12 x + y − 4z = 12  \n2x + 2 y + 5z = −15  \n(0, 0, −3)  \n8) 5a + 5b + 5c = −20  \n4a + 3b + 3c = −6  \n−4a + 3b + 3c = 9  \nNo unique solution  \n9) −6r + 5s + 2t = −11  \n−2r + s + 4t = −9  \n4r − 5s + 5t = −4  \n(4, 3, −1)  \n11) 5x − 4 y + 2z = 21  \n−x − 5 y + 6z = −24  \n−x − 4 y + 5z = −21  \n(5, −1, −4)  \n13) −3a − b − 3c = −8  \n−5a + 3b + 6c = −4  \n−6a − 4b + c = −20  \n(2, 2, 0)  \n15) 3a − 3b + 4c = −23 a + 2b − 3c = 25  \n4a − b + c = 25  \nNo unique solution  \n10) −6x − 2 y + 2z = −8  \n3x − 2 y − 4z = 8  \n6x − 2 y − 6z = −18  \nNo unique solution  \n12) 6r − s + 3t = −9  \n5r + 5s − 5t = 20  \n3r − s + 4t = −5  \n(−1, 6, 1)  \n14) −5x + 3 y + 6z = 4  \n−3x + y + 5z = −5  \n−4x + 2 y + z = 13  \n(−2, 4, −3)  \n16) −6x − 2 y − z = −17  \n5x + y − 6z = 19  \n−4x − 6 y − 6z = −20  \n(2, 3, −1)  \nCritical thinking question:  \n17) Write a system of equations with the solution (2, 1, 0) .  \nMany answers. Ex: x + y + z = 3, 2x + y + z = 5, x + 2 y − z = 4  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaigwpx2epycUm","https://ap.wps.com/l/cbCaigwpx2epycUm","pdf",34628,11,"English","en",105,"# Solve each system by elimination\n## Problems 1-16\n## Critical thinking question 17","[{\"question\":\"How do you solve each system of three equations in this worksheet?\",\"answer\":\"Use the elimination method to eliminate variables until you can solve for x, y, and z, then check consistency with the given equations.\"},{\"question\":\"What should you conclude when the worksheet says “No unique solution”?\",\"answer\":\"That indicates the system does not have exactly one solution; it may have infinitely many solutions or no solution depending on consistency.\"},{\"question\":\"What is required for the critical thinking question 17?\",\"answer\":\"Write a system of equations that has the solution (2, 1, 0), meaning all three equations are satisfied by x=2, y=1, z=0.\"}]","Solving Systems of Three Equations w/ Elimination - Worksheet | PDF",1791426161,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"solving-systems-of-three-equations-w-elimination-worksheet","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":20,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/solving-systems-of-three-equations-w-elimination-worksheet/522777/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":74,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/solving-systems-of-three-equations-w-elimination-worksheet/522777.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":118,"interactionType":119,"userInteractionCount":72},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"How do you solve each system of three equations in this worksheet?","Question",{"text":128,"@type":129},"Use the elimination method to eliminate variables until you can solve for x, y, and z, then check consistency with the given equations.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"What should you conclude when the worksheet says “No unique solution”?",{"text":133,"@type":129},"That indicates the system does not have exactly one solution; it may have infinitely many solutions or no solution depending on consistency.",{"name":135,"@type":126,"acceptedAnswer":136},"What is required for the critical thinking question 17?",{"text":137,"@type":129},"Write a system of equations that has the solution (2, 1, 0), meaning all three equations are satisfied by x=2, y=1, z=0.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":75},1791505733]