Bài 4: Giải hệ phương trình bằng phương pháp cộng đại số
Hướng dẫn giải Bài 20 (Trang 19 SGK Toán Đại số 9, Tập 2)
<p>Giải các hệ phương trình sau bằng phương pháp cộng đại số:</p>
<p>a, <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><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math>; b, <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>5</mn><mi>y</mi><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math>; c, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math>; d, <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><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math> ; e, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>0</mn><mo>,</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>0</mn><mo>,</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></p>
<p>Giải: </p>
<p>a, <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><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>5</mn><mi>x</mi><mo>=</mo><mn>10</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></p>
<p>b, <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>5</mn><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><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>5</mn><mi>y</mi><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mn>8</mn><mi>y</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><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>5</mn><mi>y</mi><mo>=</mo><mn>8</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mtable><mtr><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd></mtr></mtable></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></p>
<p>c, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></p>
<p>d, <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><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>4</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>9</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>⇔</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><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>13</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>13</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></p>
<p>e, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>0</mn><mo>,</mo><mn>3</mn><mi>x</mi><mo>+</mo><mn>0</mn><mo>,</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>15</mn></mtd></mtr><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>15</mn></mtd></mtr><mtr><mtd><mn>4</mn><mo>,</mo><mn>5</mn><mi>y</mi><mo>=</mo><mn>13</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>=</mo><mn>15</mn><mo>-</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>.</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mn>1</mn><mo>,</mo><mn>5</mn><mi>x</mi><mo>=</mo><mn>7</mn><mo>,</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></mrow></mfenced></mrow></mfenced></math></p>
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