[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-467323-105":59,"doc-detail-467323-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","identifying-point-of-intersection-with-equations","Identifying Point of Intersection with Equations","","Worksheet content focused on determining the intersection point for each of several systems of linear equations. Each item provides two equations to be used to find where the lines meet on a coordinate graph. An answer key lists the graph intersection points and also shows algebraic substitution or solving steps for x and y. Problems cover multiple slope and intercept combinations, requiring consistent calculation of x and y values.",{"@graph":69,"@context":122},[70,84,105],{"@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/identifying-point-of-intersection-with-equations/467323/",{"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/identifying-point-of-intersection-with-equations/467323.png","ImageObject",300,407,{"name":92,"@type":93},"Ezra","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main task of the worksheet?","Question",{"text":112,"@type":113},"For each system of equations, determine the point where the corresponding lines intersect on a graph.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Where can the correct answers be found?",{"text":117,"@type":113},"The document includes an answer key listing the intersection points for problems 1 through 10.",{"name":119,"@type":110,"acceptedAnswer":120},"How are the intersection points typically obtained in the answer key?",{"text":121,"@type":113},"The answer key shows solving each system by finding x first, then substituting to compute y, using the resulting equation forms.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},467323,1792877107,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39},1099514068035,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","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  --00..2x4x--24 2) {yy  --40..25x25x 88\u003Cbr>3) {yy  33..5x25+54 4) {yy  64.. 5x5x  95\u003Cbr>5) {yy  --20.. 5x5x--84 6) {yy  05.. 5x5x 64\u003Cbr>7) {yy  -006.1xx- 5 8) {yy  10.. 5x1x 77\u003Cbr>9) {yy  -00.3x3x- 1 10) {yy  10..8x4x 25 |  |  |  |  | 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 10)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 10)[ 10](Math www.CommonCoreSheets.com 10)  \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.  (-10 , 0) \u003Cbr>2.  (-4 , 9)  3.  (-4 , -9)  4.  (-2 , -4)  5.  (-2 , -3)  6.  (-2 , -7)  7.  (10 , 4)  8.  (10 , 8)  9.  (10 , -2)  10.  (5 , 7)  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) {yy  --00..2x4x--24 -0.2x-2 = -0 .4x-4\u003Cbr>0.2x = -2 1x = -10\u003Cbr>y = (-0 .2×-10)-2\u003Cbr>y = (-0 .4×-10)-4\u003Cbr>3) {yy  33..5x25+54\u003Cbr>3. 5x+5 = 3.25x+4\u003Cbr>0.25x = -1\u003Cbr>1x = -4\u003Cbr>y = (3.5×-4)+5\u003Cbr>y = (3.25×-4)+4\u003Cbr>5) {yy  --20.. 5x5x--84\u003Cbr>-2. 5x-8 = -0 . 5x-4\u003Cbr>-2x = 4 1x = -2\u003Cbr>y = (-2 . 5×-2)-8\u003Cbr>y = (-0 . 5×-2)-4\u003Cbr>7) {yy  -006.1xx- 5\u003Cbr>-0. 1x+5 = 0. 6x-2\u003Cbr>-0.7x = -7\u003Cbr>1x = 10\u003Cbr>y = (-0.1×10)+5\u003Cbr>y = (0 . 6×10)-2\u003Cbr>9) {yy  -00.3x3x- 1\u003Cbr>0.3x-5 = -0 .3x+1\u003Cbr>0. 6x = 6 1x = 10\u003Cbr>y = (0 .3×10)-5\u003Cbr>y = (-0.3×10)+1 | 2) {yy  --40..25x25x 88\u003Cbr>-4.25x-8 = -0 .25x+8\u003Cbr>-4x = 16 1x = -4\u003Cbr>y = (-4 .25×-4)-8\u003Cbr>y = (-0.25×-4)+8\u003Cbr>4) {yy  64.. 5x5x  95\u003Cbr>6. 5x+9 = 4. 5x+5 2x = -4\u003Cbr>1x = -2\u003Cbr>y = (6.5×-2)+9\u003Cbr>y = (4.5×-2)+5\u003Cbr>6) {yy  05.. 5x5x 64\u003Cbr>0. 5x-6 = 5. 5x+4\u003Cbr>-5x = 10 1x = -2\u003Cbr>y = (0 . 5×-2)-6\u003Cbr>y = (5.5×-2)+4\u003Cbr>8) {yy  10.. 5x1x 77\u003Cbr>1. 5x-7 = 0. 1x+7\u003Cbr>1.4x = 14 1x = 10\u003Cbr>y = (1 . 5×10)-7\u003Cbr>y = (0.1×10)+7\u003Cbr>10) {yy  10..8x4x 25\u003Cbr>1.8x-2 = 0.4x+5\u003Cbr>1.4x = 7 1x = 5\u003Cbr>y = (1 .8×5)-2\u003Cbr>y = (0.4×5)+5 |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  | 90 | 80 | 70 | 60 | 50 | 40 | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 10)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 10)[ 10](Math www.CommonCoreSheets.com 10)  \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  --00..2x4x--24 2) {yy  --40..25x25x 88\u003Cbr>3) {yy  33..5x25+54 4) {yy  64.. 5x5x  95\u003Cbr>5) {yy  --20.. 5x5x--84 6) {yy  05.. 5x5x 64 | 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)  \n10","cbCaimElDsCNERGj","https://ap.wps.com/l/cbCaimElDsCNERGj","pdf",42937,"English","# For each system of equations determine the point of intersection in a graph\n## Problems 1-10\n## Answer key with intersection points","[{\"question\":\"What is the main task of the worksheet?\",\"answer\":\"For each system of equations, determine the point where the corresponding lines intersect on a graph.\"},{\"question\":\"Where can the correct answers be found?\",\"answer\":\"The document includes an answer key listing the intersection points for problems 1 through 10.\"},{\"question\":\"How are the intersection points typically obtained in the answer key?\",\"answer\":\"The answer key shows solving each system by finding x first, then substituting to compute y, using the resulting equation forms.\"}]","Identifying Point of Intersection with Equations | PDF",1790772704]