Bài 2: Hệ hai phương trình bậc nhất hai ẩn
Hướng dẫn giải Bài 5 (Trang 11 SGK Toán Đại số 9, Tập 2)
<p>Đo&aacute;n nhận số nghiệm của c&aacute;c hệ phương tr&igrave;nh sau bằng h&igrave;nh học:</p> <p>a)<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi mathvariant="normal">x</mi><mo>-</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">x</mi><mo>-</mo><mn>2</mn><mi mathvariant="normal">y</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math>;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;b)<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></p> <p><strong>Giải</strong></p> <p>a)&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><mi>y</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></p> <p>Vẽ&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>d</mi><mn>1</mn></msub></mfenced></math> :&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>-</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></math></p> <p>Cho&nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>&#160;</mo><mo>&#8658;</mo><mi mathvariant="normal">y</mi><mo>=</mo><mo>-</mo><mn>1</mn></math>, ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>(</mo><mn>0</mn><mo>;</mo><mo>-</mo><mn>1</mn><mo>)</mo></math>.</p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, ta được B&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>;</mo><mo>&#160;</mo><mn>0</mn></mrow></mfenced></math>.</p> <p>V&igrave;&nbsp;<math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>d</mi><mn>2</mn></msub></mfenced></math> :&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn></math></p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>&#160;</mo></math>ta được C&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></math>.&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo></math>ta được D (<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>;</mo><mn>0</mn></mrow></mfenced></math></p> <p>Hai đường thẳng cắt nhau tại điểm M c&oacute; tọa độ&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>=</mo><mn>1</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>1</mn></mrow></mfenced></math></p> <p>Thay&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo><mi>y</mi><mo>=</mo><mn>1</mn></math> v&agrave;o c&aacute;c phương tr&igrave;nh của hệ ta được:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>1</mn><mo>-</mo><mn>1</mn><mo>=</mo><mn>1</mn><mo>&#160;</mo><mfenced><mrow><mi>t</mi><mi>h</mi><mi>&#7887;</mi><mi>a</mi></mrow></mfenced><mspace linebreak="newline"/><mn>1</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>=</mo><mo>-</mo><mn>1</mn><mfenced><mrow><mi>t</mi><mi>h</mi><mi>&#7887;</mi><mi>a</mi></mrow></mfenced></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p> <p>Vậy hệ phương tr&igrave;nh c&oacute; một nghiệm&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi mathvariant="normal">x</mi><mo>;</mo><mi mathvariant="normal">y</mi></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>1</mn><mo>;</mo><mn>1</mn></mrow></mfenced></math>.</p> <p><img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/18022022/screenshot_1-eEnsow.png" /></p> <p>b)<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mn>2</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></p> <p>Vẽ&nbsp;<math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>d</mi><mn>1</mn></msub></mfenced><mo>:</mo><mo>&#160;</mo><mn>2</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>4</mn></math></p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>y</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo>&#160;</mo></math>ta được A<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>;</mo><mn>4</mn></mrow></mfenced></math>.</p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>x</mi><mo>=</mo><mn>2</mn></math>, ta được B&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>;</mo><mn>0</mn></mrow></mfenced></math></p> <p>Vẽ&nbsp;<math style="font-family:'Times New Roman'" xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi>d</mi><mn>2</mn></msub></mfenced></math>:&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>1</mn></math></p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>y</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>&#160;</mo></math>ta được C<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>;</mo><mn>1</mn></mrow></mfenced></math>.</p> <p>Cho&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>0</mn><mo>&#8658;</mo><mi>x</mi><mo>=</mo><mn>2</mn><mo>,</mo></math> ta được D<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>;</mo><mn>0</mn></mrow></mfenced></math></p> <p>Hai đường thẳng cắt nhau tại điểm N c&oacute; tọa độ&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi mathvariant="normal">x</mi><mo>=</mo><mn>1</mn><mo>;</mo><mo>&#160;</mo><mi mathvariant="normal">y</mi><mo>=</mo><mn>2</mn></mrow></mfenced></math></p> <p>Thay&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>x=1,&#160;y=2</mtext></math> v&agrave;o c&aacute;c phương tr&igrave;nh của hệ ta được:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>4</mn><mo>&#160;</mo><mi>v</mi><mi>&#224;</mi><mo>&#160;</mo><mo>-</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>1</mn><mo>&#160;</mo><mo>(</mo><mi>t</mi><mi>h</mi><mi>&#7887;</mi><mi>a</mi><mo>)</mo></math></p> <p><img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/18022022/screenshot_2-k9wVXt.png" /></p>
Xem lời giải bài tập khác cùng bài