[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-467334-105":59,"doc-detail-467334-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-answer-key-467334","Identifying Point of Intersection with Equations - Answer Key","","Worksheets and answer key for determining the intersection point of each system of equations on a graph. Ten systems are presented with two linear equations per system, requiring solving for x and y to locate where the lines meet. The answer key provides the coordinate pair for each system, along with an algebraic process that isolates variables and substitutes to compute the intersection.",{"@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-answer-key-467334/467334/",{"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-467334/467334.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":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the worksheet ask you to find for each system of equations?","Question",{"text":112,"@type":113},"It asks you to determine the point of intersection of the two lines on a graph, expressed as a coordinate pair.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the answers provided in the answer key?",{"text":117,"@type":113},"The answer key lists the intersection coordinates for each system and shows the corresponding algebraic steps to compute them.",{"name":119,"@type":110,"acceptedAnswer":120},"What types of equations are used in these systems?",{"text":121,"@type":113},"Each system consists of two linear equations, and solving them gives the shared x- and y-values at the intersection point.","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},467334,1792877110,{"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":81,"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  10..25x25x 80 2) {yy  00..8x2x-+15\u003Cbr>3) {yy  --22..255xx-4-3 4) {yy  58.. 5x5x--17\u003Cbr>5) {yy  --31..75x25x 55 6) {yy  -002. 6xx- +13\u003Cbr>7) {yy  00..7x9x--57 8) {yy  --24..25x25x-+71\u003Cbr>9) {yy  01..75x75x  19 10) {yy  --11..75x25x  84 |  |  |  |  | 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 4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 4)[ 4](Math www.CommonCoreSheets.com 4)  \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.  (8 , 2) \u003Cbr>2.  (-10 , -3)  3.  (-4 , 6)  4.  (2 , 10)  5.  (-4 , 10)  6.  (5 , 0)  7.  (10 , 2)  8.  (-4 , 10)  9.  (-8 , -5)  10.  (8 , -6)  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 1) {yy  10..25x25x 80\u003Cbr>1.25x-8 = 0.25x+0 1x = 8\u003Cbr>1x = 8\u003Cbr>y = (1 .25×8)-8\u003Cbr>y = (0.25×8)+0\u003Cbr>3) {yy  --22..255xx-4-3\u003Cbr>-2.25x-3 = -2 . 5x-4\u003Cbr>0.25x = -1 1x = -4\u003Cbr>y = (-2 .25×-4)-3\u003Cbr>y = (-2 . 5×-4)-4\u003Cbr>5) {yy  --31..75x25x 55\u003Cbr>-3.75x-5 = -1 .25x+5\u003Cbr>-2. 5x = 10 1x = -4\u003Cbr>y = (-3 .75×-4)-5\u003Cbr>y = (-1.25×-4)+5\u003Cbr>7) {yy  00..7x9x--57\u003Cbr>0.7x-5 = 0.9x-7\u003Cbr>-0.2x = -2 1x = 10\u003Cbr>y = (0 .7×10)-5\u003Cbr>y = (0 .9×10)-7\u003Cbr>9) {yy  01..75x75x  19\u003Cbr>0.75x+1 = 1.75x+9\u003Cbr>-1x = 8\u003Cbr>1x = -8\u003Cbr>y = (0.75×-8)+1\u003Cbr>y = (1.75×-8)+9 | 2) {yy  00..8x2x-+15\u003Cbr>0.8x+5 = 0.2x-1\u003Cbr>0. 6x = -6\u003Cbr>1x = -10\u003Cbr>y = (0.8×-10)+5\u003Cbr>y = (0 .2×-10)-1\u003Cbr>4) {yy  58.. 5x5x--17\u003Cbr>5. 5x-1 = 8. 5x-7\u003Cbr>-3x = -6 1x = 2\u003Cbr>y = (5 . 5×2)-1\u003Cbr>y = (8 . 5×2)-7\u003Cbr>6) {yy  -002. 6xx- +13\u003Cbr>-0. 6x+3 = 0.2x-1\u003Cbr>-0.8x = -4\u003Cbr>1x = 5\u003Cbr>y = (-0.6×5)+3\u003Cbr>y = (0 .2×5)-1\u003Cbr>8) {yy  --24..25x25x-+71\u003Cbr>-2.25x+1 = -4 .25x-7 2x = -8\u003Cbr>1x = -4\u003Cbr>y = (-2.25×-4)+1\u003Cbr>y = (-4 .25×-4)-7\u003Cbr>10) {yy  --11..75x25x  84\u003Cbr>-1.75x+8 = -1 .25x+4\u003Cbr>-0. 5x = -4\u003Cbr>1x = 8\u003Cbr>y = (-1.75×8)+8\u003Cbr>y = (-1.25×8)+4 |  |  |  |  |  |  |  |  |  |  |\n| 1-10 |  | 90 | 80 | 70 | 60 | 50 | 40 | 30 | 20 | 10 | 0 |\n\n[Math](Math www.CommonCoreSheets.com 4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 4)[ 4](Math www.CommonCoreSheets.com 4)  \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  10..25x25x 80 2) {yy  00..8x2x-+15\u003Cbr>3) {yy  --22..255xx-4-3 4) {yy  58.. 5x5x--17\u003Cbr>5) {yy  --31..75x25x 55 6) {yy  -002. 6xx- +13 | 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)  \n4","cbCaijivN9w5ib2f","https://ap.wps.com/l/cbCaijivN9w5ib2f","pdf",43016,"English","# For each system of equations\n## Determine the point of intersection in a graph\n## Answers and solution steps","[{\"question\":\"What does the worksheet ask you to find for each system of equations?\",\"answer\":\"It asks you to determine the point of intersection of the two lines on a graph, expressed as a coordinate pair.\"},{\"question\":\"How are the answers provided in the answer key?\",\"answer\":\"The answer key lists the intersection coordinates for each system and shows the corresponding algebraic steps to compute them.\"},{\"question\":\"What types of equations are used in these systems?\",\"answer\":\"Each system consists of two linear equations, and solving them gives the shared x- and y-values at the intersection point.\"}]","Identifying Point of Intersection with Equations - Answer Key | PDF",1790772716]