[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-464135-105":3,"doc-detail-464135-en":80,"detail-sidebar-cat-0-en-105":95},{"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":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","identifying-point-of-intersection-with-equations-worksheet-answers","Identifying Point of Intersection with Equations - Worksheet Answers","","Worksheet focused on finding the intersection point for multiple systems of linear equations on a coordinate graph. Each item presents two equations that form a system, requiring solving the equations and identifying the shared x- and y-values where the lines cross. An answer key lists the resulting ordered pairs for every system, supporting self-checking and quick verification of graph intersection accuracy across varied slopes and intercepts.",{"@graph":14,"@context":72},[15,34,55],{"@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/identifying-point-of-intersection-with-equations-worksheet-answers/464135/",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/identifying-point-of-intersection-with-equations-worksheet-answers/464135.png","ImageObject",300,407,{"name":42,"@type":43},"Finn","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-30",true,{"@type":52,"interactionType":53,"userInteractionCount":30},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What do you need to find for each system of equations?","Question",{"text":62,"@type":63},"Find the point where the two lines intersect on a coordinate graph, expressed as an ordered pair (x, y).","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How is the answer for each system represented?",{"text":67,"@type":63},"Each solution is given as an ordered pair, such as (2, 5), showing the intersection coordinates.",{"name":69,"@type":60,"acceptedAnswer":70},"What is the purpose of the included answer key?",{"text":71,"@type":63},"It provides the correct ordered-pair intersection points for all listed systems so learners can check their work.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},464135,1790767722,{"code":4,"msg":81,"data":82},"success",{"doc_id":78,"user_id":83,"nickname":42,"user_avatar":84,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":85,"file_id":86,"file_url":87,"file_type":88,"file_size":89,"view_count":30,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":90,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":91,"faqs":92,"seo_title":93,"seo_description":12,"update_tm":79,"read_time":94},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","Identifying Point of Intersection with Equations  \nName:  \n\n| For each system of equations determine the point of intersection in a graph.\u003Cbr>1) {yy  15.. 5x5x-+62 2) {yy  00..7x6x--23\u003Cbr>3) {yy  --00.. 5x6x--43 4) {yy  --43..5x25x-9-4\u003Cbr>5) {yy  -009. 5xx+-59 6) {yy  -00.1x5x- +15\u003Cbr>7) {yy  -00.1x2x++96 8) {yy  00..5x75x- -57\u003Cbr>9) {yy  -022. 5x5x+-29 10) {yy  43..25x25x--95 |  |  |  |  | Answers\u003Cbr>1.  \u003Cbr>2.  \u003Cbr>3.  \u003Cbr>4.  \u003Cbr>5.  \u003Cbr>6.  \u003Cbr>7.  \u003Cbr>8.  \u003Cbr>9.  \u003Cbr>10.   |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1-10 | 90 | 80 | 70 | 60 | 50 | 40 | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 1)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 1)[ 1](Math www.CommonCoreSheets.com 1)  \nIdentifying Point of Intersection with Equations  \nName: Answer Key  \n\n| For each system of equations determine the point of intersection in a graph. |  |  |  |  |  | Answers 1.  (2 , 5) \u003Cbr>2.  (-10 , -9)  3.  (10 , -9)  4.  (-4 , 9)  5.  (-10 , 0)  6.  (10 , 0)  7.  (-10 , 8)  8.  (8 , -1)  9.  (4 , 0)  10.  (4 , 8)  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) {yy  15.. 5x5x-+62\u003Cbr>1. 5x+2 = 5. 5x-6\u003Cbr>-4x = -8\u003Cbr>1x = 2\u003Cbr>y = (1.5×2)+2\u003Cbr>y = (5 . 5×2)-6\u003Cbr>3) {yy  --00.. 5x6x--43 -0. 5x-4 = -0 . 6x-3\u003Cbr>0. 1x = 1 1x = 10\u003Cbr>y = (-0 . 5×10)-4\u003Cbr>y = (-0 . 6×10)-3\u003Cbr>5) {yy  -009. 5xx+-59\u003Cbr>-0. 5x-5 = 0.9x+9\u003Cbr>-1.4x = 14 1x = -10\u003Cbr>y = (-0 . 5×-10)-5\u003Cbr>y = (0.9×-10)+9\u003Cbr>7) {yy  -00.1x2x++96\u003Cbr>0. 1x+9 = -0 .2x+6\u003Cbr>0.3x = -3\u003Cbr>1x = -10\u003Cbr>y = (0.1×-10)+9\u003Cbr>y = (-0.2×-10)+6\u003Cbr>9) {yy  -022. 5x5x+-29\u003Cbr>-0. 5x+2 = 2.25x-9\u003Cbr>-2.75x = -11\u003Cbr>1x = 4\u003Cbr>y = (-0.5×4)+2\u003Cbr>y = (2 .25×4)-9 | 2) {yy  00..7x6x--23\u003Cbr>0.7x-2 = 0. 6x-3\u003Cbr>0. 1x = -1 1x = -10\u003Cbr>y = (0 .7×-10)-2\u003Cbr>y = (0 . 6×-10)-3\u003Cbr>4) {yy  --43..5x25x-9-4\u003Cbr>-4. 5x-9 = -3 .25x-4\u003Cbr>-1.25x = 5 1x = -4\u003Cbr>y = (-4 . 5×-4)-9\u003Cbr>y = (-3 .25×-4)-4\u003Cbr>6) {yy  -00.1x5x- +15\u003Cbr>0. 1x-1 = -0 . 5x+5\u003Cbr>0. 6x = 6 1x = 10\u003Cbr>y = (0 . 1×10)-1\u003Cbr>y = (-0.5×10)+5\u003Cbr>8) {yy  00..5x75x- -57\u003Cbr>0. 5x-5 = 0.75x-7\u003Cbr>-0.25x = -2 1x = 8\u003Cbr>y = (0 . 5×8)-5\u003Cbr>y = (0 .75×8)-7\u003Cbr>10) {yy  43..25x25x--95 4.25x-9 = 3.25x-5 1x = 4\u003Cbr>1x = 4\u003Cbr>y = (4 .25×4)-9\u003Cbr>y = (3 .25×4)-5 |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  | 90 | 80 | 70 | 60 | 50 | 40 | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 1)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 1)[ 1](Math www.CommonCoreSheets.com 1)  \nIdentifying Point of Intersection with Equations  \nName:  \n\n| For each system of equations determine the point of intersection in a graph.\u003Cbr>1) {yy  15.. 5x5x-+62 2) {yy  00..7x6x--23\u003Cbr>3) {yy  --00.. 5x6x--43 4) {yy  --43..5x25x-9-4\u003Cbr>5) {yy  -009. 5xx+-59 6) {yy  -00.1x5x- +15 | 1.\u003Cbr>2.\u003Cbr>3.\u003Cbr>4.\u003Cbr>5.\u003Cbr>6. |  | Answers |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |\n| 1-6 | 83 | 67 |  | 50 | 33 | 17 | 0 |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n1","cbCailmUf6iBL3e8","https://ap.wps.com/l/cbCailmUf6iBL3e8","pdf",43019,"English","# For each system of equations determine the point of intersection in a graph","[{\"question\":\"What do you need to find for each system of equations?\",\"answer\":\"Find the point where the two lines intersect on a coordinate graph, expressed as an ordered pair (x, y).\"},{\"question\":\"How is the answer for each system represented?\",\"answer\":\"Each solution is given as an ordered pair, such as (2, 5), showing the intersection coordinates.\"},{\"question\":\"What is the purpose of the included answer key?\",\"answer\":\"It provides the correct ordered-pair intersection points for all listed systems so learners can check their work.\"}]","Identifying Point of Intersection with Equations - Worksheet Answers | PDF",8,{"code":4,"msg":81,"data":96},[97,101,105,108,113,118,123,127,132,135,139],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":106,"slug":107},70,"exam",{"id":109,"doc_module":4,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},5,"Comic",60,"comic",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},6,"Technology",50,"technology",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},7,"Healthcare",40,"healthcare",{"id":94,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":125,"slug":126},"Research & Report",30,"research-report",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":130,"slug":131},9,"Religion & Spirituality",20,"religion-spirituality",{"id":130,"doc_module":4,"doc_module_name":25,"category_name":133,"show_sort_weight":130,"slug":134},"World Cup","world-cup",{"id":136,"doc_module":4,"doc_module_name":25,"category_name":137,"show_sort_weight":136,"slug":138},10,"Lifestyle","lifestyle",{"id":140,"doc_module":4,"doc_module_name":25,"category_name":141,"show_sort_weight":109,"slug":142},19,"General","general"]