Bài 4: Giải hệ phương trình bằng phương pháp cộng đại số
Hướng dẫn giải Bài 22 (Trang 19 SGK Toán Đại số 9, Tập 2)
<p>Giải c&aacute;c hệ phương tr&igrave;nh sau bằng phương ph&aacute;p cộng đại số:</p> <p>a,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mo>-</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>6</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mi>b</mi><mo>,</mo><mo>&#160;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>11</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mo>&#160;</mo><mi>c</mi><mo>,</mo><mo>&#160;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>y</mi><mo>=</mo><mn>3</mn><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></p> <p>Giải:</p> <p>a,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mo>-</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>6</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mo>-</mo><mn>15</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>12</mn></mtd></mtr><mtr><mtd><mn>12</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>14</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mo>-</mo><mn>3</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>15</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>12</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mn>6</mn><mi>y</mi><mo>=</mo><mn>12</mn><mo>+</mo><mn>15</mn><mo>.</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr></mtable><mo>&#8660;</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mn>6</mn><mi>y</mi><mo>=</mo><mn>22</mn></mtd></mtr></mtable><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mfrac><mn>11</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></mrow></mfenced></mrow></mfenced></math></p> <p>b,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>11</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>22</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>22</mn></mtd></mtr><mtr><mtd><mn>4</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>22</mn></mtd></mtr><mtr><mtd><mn>0</mn><mi>x</mi><mo>-</mo><mn>0</mn><mi>y</mi><mo>=</mo><mn>27</mn></mtd></mtr></mtable></mfenced><mspace linebreak="newline"/></math></p> <p>Hệ phương tr&igrave;nh v&ocirc; nghiệm.</p> <p>c,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mi>y</mi><mo>=</mo><mn>3</mn><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>3</mn><mo>.</mo><mfrac><mn>10</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>10</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>&#8712;</mo><mi>R</mi></mtd></mtr><mtr><mtd><mn>2</mn><mi>y</mi><mo>=</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>10</mn></mtd></mtr></mtable></mfenced><mo>&#8660;</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>&#8712;</mo><mi>R</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>x</mi><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></p> <p>Hệ phương tr&igrave;nh c&oacute; v&ocirc; số nghiệm.</p>
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