Bài 1: Phương trình bậc nhất hai ẩn
Hướng dẫn giải Bài 2 (Trang 7 SGK Toán Đại số 9, Tập 2)
<p>Với mỗi phương trình sau, tìm nghiệm tổng quát của phương trình và vẽ đường thẳng biểu diễn tập nghiệm của nó :</p>
<p>a) 3x - y = 2 ; b) x+ 5y = 3 ;</p>
<p>c) 4x - 3y = -1 ; d) x + 5y = 0 ;</p>
<p>e) 4x + 0y = -2 ; f) 0x + 2y = 5.</p>
<p><strong>Giải</strong></p>
<p>a) Ta có phương trình 3x - 2y = 2 (1)</p>
<p>Vì (1) <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 mathvariant="normal">x</mi><mo> </mo><mo>∈</mo><mi mathvariant="normal">ℝ</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn></mtd></mtr></mtable></mfenced></math>nên nghiệm tổng quát của phương trình là: </p>
<p>(x; 3x-2) hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>∈</mo><mo> </mo><mi mathvariant="normal">ℝ</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mn>2</mn></mtd></mtr></mtable></mfenced></math> <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/2a27d27b-8a47-4490-85fb-a2bf8fb92925.PNG" /></p>
<p>*Vẽ đường thẳng biểu diễn tập nghiệm của phương trình: </p>
<p>Với y = 3x - 2</p>
<p>Cho x = 0 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math> y = -2 được A (0; -2).</p>
<p style="line-height: 1.1;">Cho y = 0 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math>3x = 2 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo></math>x = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac></math> ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>;</mo><mo> </mo><mn>0</mn></mrow></mfenced></math>.</p>
<p>Biểu diễn cặp số A(0; -2) và <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>;</mo><mo> </mo><mn>0</mn></mrow></mfenced></math> trên hệ trục tọa độ và đường thẳng AB chính là tập nghiệm của phương trình 3x - y = 2.</p>
<p>b) x + 5y = 3 <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 mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>5</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>∈</mo><mi mathvariant="normal">ℝ</mi></mtd></mtr></mtable></mfenced></math></p>
<p>Ta được nghiệm tổng quát của phương trình là (-5y + 3, y).</p>
<p>hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>5</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>+</mo><mo> </mo><mn>3</mn></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>∈</mo><mi mathvariant="normal">ℝ</mi></mtd></mtr></mtable></mfenced></math> <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/4595a369-5074-405c-8097-784ea72cbea7.PNG" /></p>
<p>Biểu diễn hình học: tập nghiệm là đường thẳng AB với A(3; 0); B(-2; 1).</p>
<p>c) 4x - 3y = -1 <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 mathvariant="normal">x</mi><mo> </mo><mo>∈</mo><mo> </mo><mi mathvariant="normal">ℝ</mi><mo> </mo></mtd></mtr><mtr><mtd><mn>3</mn><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></p>
<p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>∈</mo><mo> </mo><mi mathvariant="normal">ℝ</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math> <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/929930dc-c006-410a-be99-ac6ce088a14d.PNG" /></p>
<p>Tập nghiệm là đường thẳng qua <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mfenced><mrow><mn>0</mn><mo>;</mo><mo> </mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></mfenced><mo> </mo><mi>và</mi><mo> </mo><mi mathvariant="normal">B</mi><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>;</mo><mo> </mo><mn>0</mn></mrow></mfenced></math> </p>
<p>d) x +5y = 0 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mn>5</mn><mi mathvariant="normal">y</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>∈</mo><mo> </mo><mi mathvariant="normal">ℝ</mi></mtd></mtr></mtable></mfenced></math> </p>
<p>Tập nghiệm là đường thẳng đi qua O(0; 0) và A(-5; 1). <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/701b9a02-5c69-4341-8755-73c82b7b963b.PNG" /></p>
<p>e) 4x + 0y = -2 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>∈</mo><mo> </mo><mi mathvariant="normal">ℝ</mi></mtd></mtr></mtable></mfenced></math></p>
<p>Tập nghiệm là đường thẳng x = <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math>, qua <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>;</mo><mo> </mo><mn>0</mn></mrow></mfenced></math> và song song với trục tung.<img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/17022022/6d74143f-c7c4-45df-8617-4eb5880c5b7d.PNG" /></p>
<p>f) 0x + 2y = 5 <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇔</mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">x</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math> </p>
<p>Tập nghiệm là đường thẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo></math> qua <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>;</mo><mo> </mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mrow></mfenced></math> và song song với trục hoành.<img class="wscnph" src="data:image/png;base64,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" width="135" height="118" /></p>
<p> </p>
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