{"id":616937,"date":"2023-06-20T10:46:32","date_gmt":"2023-06-20T05:16:32","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-value-of-k-for-which-the-equations-2x-3y-7-and-k-1-x-k-2-y-3k-has-an-infinite-number-of-solutions-is-____\/"},"modified":"2025-06-26T17:44:21","modified_gmt":"2025-06-26T12:14:21","slug":"the-value-of-k-for-which-the-equations-2x-3y-7-and-k-1-x-k-2-y-3k-has-an-infinite-number-of-solutions-is-____","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-value-of-k-for-which-the-equations-2x--3y--7-and-k--\/","title":{"rendered":"The value of k for which the equations 2x + 3y = 7 and (k &#8211; 1) x + (k + 2) y = 3k has an infinite number of solutions is ____."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The value of k for which the equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k has an infinite number of solutions is ____.","custom_permalink":"question\/mathematics\/the-value-of-k-for-which-the-equations-2x--3y--7-and-k--\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt; line-height:normal\"><span>The value of k for which the equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k has an infinite number of solutions is ____.<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><spanstyle=\"-aw-import:ignore\"><p><\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":null,"solution":"<span>The value of k for which the equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k has an infinite number of solutions is 7.<\/span><br><span>Given 2 equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k.<\/span><br><span>Simplifying equation 1,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mtable columnalign=\"left\" equalrows=\"true\" equalcolumns=\"true\">\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mn>2<\/m:mn><m:mi>x<\/m:mi><m:mo>+<\/m:mo><m:mn>3<\/m:mn><m:mi>y<\/m:mi><m:mo>=<\/m:mo><m:mn>7<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mo>\u21d2<\/m:mo><m:mn>2<\/m:mn><m:mi>x<\/m:mi><m:mo>+<\/m:mo><m:mn>3<\/m:mn><m:mi>y<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>7<\/m:mn><m:mo>=<\/m:mo><m:mn>0<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    \r\n   <\/m:mtable><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>&nbsp; <\/span><span>Simplifying equation 2, <\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mtable columnalign=\"left\" equalrows=\"true\" equalcolumns=\"true\">\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>1<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><m:mi>x<\/m:mi><m:mo>+<\/m:mo><m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>+<\/m:mo><m:mn>2<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><m:mi>y<\/m:mi><m:mo>=<\/m:mo><m:mn>3<\/m:mn><m:mi>k<\/m:mi><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mo>\u21d2<\/m:mo><m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>1<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><m:mi>x<\/m:mi><m:mo>+<\/m:mo><m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>+<\/m:mo><m:mn>2<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><m:mi>y<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>3<\/m:mn><m:mi>k<\/m:mi><m:mo>=<\/m:mo><m:mn>0<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    \r\n   <\/m:mtable><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<br><span>Now on comparing with standard equations,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:msub>\r\n      <m:mi>a<\/m:mi>\r\n      <m:mn>1<\/m:mn>\r\n     <\/m:msub>\r\n     <m:mo>=<\/m:mo><m:mn>2<\/m:mn><m:mo>,<\/m:mo><m:msub>\r\n      <m:mi>b<\/m:mi>\r\n      <m:mn>1<\/m:mn>\r\n     <\/m:msub>\r\n     <m:mo>=<\/m:mo><m:mn>3<\/m:mn><m:msub>\r\n      <m:mi>c<\/m:mi>\r\n      <m:mn>1<\/m:mn>\r\n     <\/m:msub>\r\n     <m:mo>=<\/m:mo><m:mo>\u2212<\/m:mo><m:mn>7<\/m:mn>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:msub>\r\n      <m:mi>a<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msub>\r\n     <m:mo>=<\/m:mo><m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>1<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><m:mo>,<\/m:mo><m:msub>\r\n      <m:mi>b<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msub>\r\n     <m:mo>=<\/m:mo><m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>+<\/m:mo><m:mn>2<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><m:mo>,<\/m:mo><m:msub>\r\n      <m:mi>c<\/m:mi>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:msub>\r\n     <m:mo>=<\/m:mo><m:mo>\u2212<\/m:mo><m:mn>3<\/m:mn><m:mi>k<\/m:mi>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>The condition for infinite solutions is, <\/span><br><img src=\"data:image\/jpeg;base64,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\" width=\"250\" height=\"140\" alt=\"\" class=\"image_resized\" style=\"width:250px;height:140px\"><span> <\/span><span>Consider case 1,<\/span><br>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mtable columnalign=\"left\" equalrows=\"true\" equalcolumns=\"true\">\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mfrac>\r\n        <m:mn>2<\/m:mn>\r\n        <m:mrow>\r\n         <m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>1<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><\/m:mrow>\r\n       <\/m:mfrac>\r\n       <m:mo>=<\/m:mo><m:mfrac>\r\n        <m:mn>3<\/m:mn>\r\n        <m:mrow>\r\n         <m:mo stretchy=\"false\">(<\/m:mo><m:mi>k<\/m:mi><m:mo>+<\/m:mo><m:mn>2<\/m:mn><m:mo stretchy=\"false\">)<\/m:mo><\/m:mrow>\r\n       <\/m:mfrac>\r\n       <\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mo>\u21d2<\/m:mo><m:mn>2<\/m:mn><m:mi>k<\/m:mi><m:mo>+<\/m:mo><m:mn>4<\/m:mn><m:mo>=<\/m:mo><m:mn>3<\/m:mn><m:mi>k<\/m:mi><m:mo>\u2212<\/m:mo><m:mn>3<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    <m:mtr columnalign=\"left\">\r\n     <m:mtd columnalign=\"left\">\r\n      <m:mrow>\r\n       <m:mo>\u21d2<\/m:mo><m:mi>k<\/m:mi><m:mo>=<\/m:mo><m:mn>7<\/m:mn><\/m:mrow>\r\n     <\/m:mtd>\r\n    <\/m:mtr>\r\n    \r\n   <\/m:mtable><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span> <\/span><span>Hence, the value of k is 7.<\/span><br><span>&nbsp;<\/span>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The value of k for which the equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k has an infinite number of solutions is ____. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The value of k for which the equations 2x + 3y = 7 and (k - 1) 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