[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-467328-105":59,"doc-detail-467328-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","identifying-point-of-intersection-with-equations-answer-key","Identifying Point of Intersection with Equations - Answer Key","","Systems of equations problems focused on finding the point of intersection on a graph. Each item provides two linear equations, then prompts determining the shared solution where both lines meet. The answer keys supply the intersection coordinates for multiple problem sets, enabling verification of the solved x- and y-values through substitution or elimination. Used for practice and assessment of coordinate geometry and linear equation solving skills.",{"@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/identifying-point-of-intersection-with-equations-answer-key/467328/",{"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-answer-key/467328.png","ImageObject",300,407,{"name":92,"@type":93},"Ezra","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does the worksheet ask you to find for each system of equations?","Question",{"text":113,"@type":114},"It asks you to determine the point of intersection on a graph for each pair of equations.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What information do the answer keys provide?",{"text":118,"@type":114},"The answer keys provide the intersection coordinates (x, y) for each system.",{"name":120,"@type":111,"acceptedAnswer":121},"How are the intersection coordinates determined?",{"text":122,"@type":114},"The intersection coordinates come from solving the two linear equations so that both equations are satisfied at the same (x, y) point.","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},467328,1791668759,{"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":41,"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},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  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  \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  -006.1xx+-34 2) {yy  -0.0 11xx--79\u003Cbr>3) {yy  --40..25x75x-+59 4) {yy  --10..5x25-82\u003Cbr>5) {yy  --21.. 5x5x--86 6) {yy  --22..255xx- -65\u003Cbr>7) {yy  --22..25x75x--57 8) {yy  --29.. 5x5x 59\u003Cbr>9) {yy  -00.7x4x- 9 10) {yy  -008.1xx- 4 |  |  |  |  | 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 2)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 2)[ 2](Math www.CommonCoreSheets.com 2)  \nIdentifying Point of Intersection with Equations  \nName: Answer Key  \n","cbCaipyGkEsjYZFg","https://ap.wps.com/l/cbCaipyGkEsjYZFg","pdf",437054,"English","# Identifying Point of Intersection with Equations\n## Problem sets\n## Answer keys (coordinates)","[{\"question\":\"What does the worksheet ask you to find for each system of equations?\",\"answer\":\"It asks you to determine the point of intersection on a graph for each pair of equations.\"},{\"question\":\"What information do the answer keys provide?\",\"answer\":\"The answer keys provide the intersection coordinates (x, y) for each system.\"},{\"question\":\"How are the intersection coordinates determined?\",\"answer\":\"The intersection coordinates come from solving the two linear equations so that both equations are satisfied at the same (x, y) point.\"}]","Identifying Point of Intersection with Equations - Answer Key | PDF",1790772709,76]