{"id":358735,"date":"2023-01-07T01:54:19","date_gmt":"2023-01-06T20:24:19","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/solve-graphically-the-pair-of-linear-equations-3%f0%9d%91%a5-%e2%88%92-4%f0%9d%91%a6-3-0-and-3%f0%9d%91%a5-4%f0%9d%91%a6-%e2%88%92-21-0-find-the-coordinates-of-the-vertices-of-the-tri\/"},"modified":"2025-06-26T14:48:43","modified_gmt":"2025-06-26T09:18:43","slug":"solve-graphically-the-pair-of-linear-equations-3%f0%9d%91%a5-%e2%88%92-4%f0%9d%91%a6-3-0-and-3%f0%9d%91%a5-4%f0%9d%91%a6-%e2%88%92-21-0-find-the-coordinates-of-the-vertices-of-the-tri","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/","title":{"rendered":"Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":": Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle.","custom_permalink":"question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/"},"categories":[],"acf":{"question":"

: Solve graphically the pair of linear equations : <\/p>

3\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.<\/p>

Find the coordinates of the vertices of the triangular region formed by these lines and x-axis. <\/p>

Also, calculate the area of this triangle.<\/p>","options":null,"solution":"

We need to graphically solve the given pair of linear equations<\/a> and find the coordinates and area of the triangle region. <\/p>

In order to draw the graphs, we need to find out two points with their \ud835\udc65 and \ud835\udc66 coordinates that satisfy the equations respectively. We will do this by putting random value of \ud835\udc65 and finding corresponding value of \ud835\udc66. <\/p>

For 3\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 or 3\ud835\udc65 \u2212 4\ud835\udc66 =\u2212 3, it can be written as<\/p>

y<\/mi>=<\/mo>3<\/mn>x<\/mi>+<\/mo>3<\/mn><\/mrow>4<\/mn><\/mfrac><\/math><\/p>
<\/figure>

For 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0 or 3\ud835\udc65 + 4\ud835\udc66 = 21, it can be written as<\/p>

y<\/mi>=<\/mo>21<\/mn>\u2212<\/mo>3<\/mn>x<\/mi><\/mrow>4<\/mn><\/mfrac><\/math><\/p>
<\/figure>

Now, putting these coordinates on a graph and joining and extending them will give us the equation. <\/p>

On plotting the point, we get the graph as<\/p>

<\/figure>

Since the curves intersect at the point (3, 3), the solution of the equations<\/p>

3\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0 \ud835\udc56\ud835\udc60 (3, 3). <\/p>

Hence, \ud835\udc65 = 3 \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc66 = 3. <\/p>

From the graph, the vertices of the triangular region are (3, 3), (\u2212 1, 0) and (7, 0). <\/p>

The area of the triangular region is<\/p>

A<\/mi>=<\/mo>1<\/mn>2<\/mn><\/mfrac>\u00d7<\/mo> base <\/mtext>\u00d7<\/mo> height <\/mtext><\/math><\/p>

On substituting the values, we get the area as<\/p>

A<\/mi>=<\/mo>1<\/mn>2<\/mn><\/mfrac>\u00d7<\/mo>8<\/mtext>\u00d7<\/mo> 3<\/mtext><\/math><\/p>

\u21d2 \ud835\udc34 = 12 \ud835\udc60\ud835\udc5e. \ud835\udc62\ud835\udc5b\ud835\udc56\ud835\udc61\ud835\udc60<\/p>","subject":""},"yoast_head":"\nSolve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\": Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle. - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\": Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-26T09:18:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle. - Infinity Learn by Sri Chaitanya","description":": Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/","og_locale":"en_US","og_type":"article","og_title":"Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle. - Infinity Learn by Sri Chaitanya","og_description":": Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle.","og_url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_modified_time":"2025-06-26T09:18:43+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/-solve-graphically-the-pair-of-linear-equations-3--4\/","name":"Solve graphically the pair of linear equations :\u00a03\ud835\udc65 \u2212 4\ud835\udc66 + 3 = 0 and 3\ud835\udc65 + 4\ud835\udc66 \u2212 21 = 0.Find the coordinates of the vertices of the triangular region formed by these lines and x-axis.\u00a0Also, calculate the area of this triangle. - 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