[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-366140-105":59,"doc-detail-366140-en":131},{"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":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","lesson-guide-solving-linear-systems","Lesson Guide - Solving Linear Systems","","Lesson guide for the video lesson “Solving Linear Systems,” focusing on key concepts and solution types for systems of linear equations. Explains how to define a linear system, what it means to find a solution, and how many solutions can exist. Covers three cases using coordinate-plane behavior: one intersection point (one solution), parallel lines with no intersection (no solution), and overlapping lines that represent the same equation (infinitely many solutions). Includes three worked examples plus a “Try On Your Own” problem and an answer key.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/lesson-guide-solving-linear-systems/366140/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/lesson-guide-solving-linear-systems/366140.png","ImageObject",300,407,{"name":92,"@type":93},"anakgang17","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is a linear system?","Question",{"text":113,"@type":114},"A linear system consists of two linear functions in the coordinate plane that you treat as a system to solve together.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How many possible solutions can a linear system have?",{"text":118,"@type":114},"A linear system can have one solution, no solution, or infinitely many solutions.",{"name":120,"@type":111,"acceptedAnswer":121},"How do you tell whether a system has one, none, or infinitely many solutions?",{"text":122,"@type":114},"If the lines intersect at exactly one point, there is one solution. If they are parallel and never intersect, there is no solution. If they overlap and represent the same function, there are infinitely many solutions.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},366140,1790432993,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},962090883568,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Name:    \nLesson Guide  \nThis lesson guide accompanies the following video lesson:  \nSolving Linear Systems  \nKey Questions  \n• What is a linear system?  \n• What is the solution to a system of linear equations?  \n• How many possible solutions exist for a linear system?  \nTypes of Solutions to Linear Systems  \nFor a given system with two linear functions on the coordinate plane, there are   possible types of solutions.  \nThe linear functions intersect at one, and only one, point. This point is the solution to the linear system.  \nThe linear functions are parallel (they have the same slope) and, therefore, never intersect. There is no solution in this case.  \nThe linear functions are overlapping (which means they are both the same function) . These systems have an infinite amount of possible solutions.  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 1  \nExample \\#1: One Solution  \nFind the solution (if any) to the linear system:  \n􀀡 = 􀀡􀀢 + 􀀡  \n􀀡 = − 􀀡􀀡 􀀡 + 􀀡  \nCHECK  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 2  \nExample \\#2: No Solution  \nFind the solution (if any) to the linear system:  \n􀀡 = 􀀡􀀡 􀀡 + 􀀡􀀡􀀡 = 􀀡􀀡 − 􀀡􀀢  \nCHECK  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 3  \nExample \\#3: Infinitely Many Solutions Find the solution (if any) to the linear system:  \n􀀡 = −􀀡􀀡 − 􀀡  \n􀀡 + 􀀡 = −􀀡􀀢  \nCHECK  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 4  \nTry On Your Own!  \nFind the solution (if any) to the linear system:  \n􀀡 = 􀀡􀀡 􀀡 − 􀀡􀀡  \n􀀡 + 􀀡􀀢 = 􀀡  \nCHECK  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 5  \nANSWER KEY  \nExample \\#1 : One Solution: (2,5)  \nExample \\#2: No Solution (parallel lines) Example \\#3: Infinitely Many Solutions Try On Your Own!: One Solution (3,-9)  \nMashup Math LLC | All Rights Reserved | Get More K-12 Math Worksheets [at ](at www.mashupmath.com)[www.mashupmath.com](at www.mashupmath.com) 6","cbCaiqWMfrV0v8Tt","https://ap.wps.com/l/cbCaiqWMfrV0v8Tt","pdf",1548169,"English","# Key Questions\n# Types of Solutions to Linear Systems\n## Example #1: One Solution\n## Example #2: No Solution\n## Example #3: Infinitely Many Solutions\n# Try On Your Own!\n# Answer Key","[{\"question\":\"What is a linear system?\",\"answer\":\"A linear system consists of two linear functions in the coordinate plane that you treat as a system to solve together.\"},{\"question\":\"How many possible solutions can a linear system have?\",\"answer\":\"A linear system can have one solution, no solution, or infinitely many solutions.\"},{\"question\":\"How do you tell whether a system has one, none, or infinitely many solutions?\",\"answer\":\"If the lines intersect at exactly one point, there is one solution. If they are parallel and never intersect, there is no solution. If they overlap and represent the same function, there are infinitely many solutions.\"}]","Lesson Guide - Solving Linear Systems | PDF",1790163963,15]