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Домножим второе уравнение на 2 и из первого уравнения вычтем второе:
![left { {{2x_1+x_2=10} atop {x_1-2x_2=8 | cdot 2}} right. \
left { {{2x_1+x_2=10} atop {2x_1-4x_2=16}} right. \\
x_2-(-4x_2)=10-16\\
x_2+4x_2=-6\\
5x_2=-6\\
x_2=- frac{6}{5} \\
x_1=8+2x_2\\
x_1=8+2cdot(- frac{6}{5})\\
x_1=8-frac{12}{5}\\
x_1= frac{40}{5} -frac{12}{5}\\
x_1= frac{28}{5} left { {{2x_1+x_2=10} atop {x_1-2x_2=8 | cdot 2}} right. \
left { {{2x_1+x_2=10} atop {2x_1-4x_2=16}} right. \\
x_2-(-4x_2)=10-16\\
x_2+4x_2=-6\\
5x_2=-6\\
x_2=- frac{6}{5} \\
x_1=8+2x_2\\
x_1=8+2cdot(- frac{6}{5})\\
x_1=8-frac{12}{5}\\
x_1= frac{40}{5} -frac{12}{5}\\
x_1= frac{28}{5}](https://tex.z-dn.net/?f=+left+%7B+%7B%7B2x_1%2Bx_2%3D10%7D+atop+%7Bx_1-2x_2%3D8+%7C+cdot+2%7D%7D+right.+%5C%0A+left+%7B+%7B%7B2x_1%2Bx_2%3D10%7D+atop+%7B2x_1-4x_2%3D16%7D%7D+right.+%5C%5C%0Ax_2-%28-4x_2%29%3D10-16%5C%5C%0Ax_2%2B4x_2%3D-6%5C%5C%0A5x_2%3D-6%5C%5C%0Ax_2%3D-+frac%7B6%7D%7B5%7D+%5C%5C%0Ax_1%3D8%2B2x_2%5C%5C%0Ax_1%3D8%2B2cdot%28-+frac%7B6%7D%7B5%7D%29%5C%5C%0Ax_1%3D8-frac%7B12%7D%7B5%7D%5C%5C%0Ax_1%3D+frac%7B40%7D%7B5%7D+-frac%7B12%7D%7B5%7D%5C%5C%0Ax_1%3D+frac%7B28%7D%7B5%7D+)
Проверка:
![left { {{2cdot frac{28}{5}- frac{6}{5} =10} atop {frac{28}{5}-2 cdot (- frac{6}{5} )=8 }} right. \ \
left { {{frac{56}{5}- frac{6}{5} =10} atop {frac{28}{5}+ frac{12}{5} =8 }} right. \ \
left { {{frac{50}{5} =10} atop {frac{40}{5} =8 }} right. \ \
left { {{10 =10} atop {8 =8 }} right. \ \ left { {{2cdot frac{28}{5}- frac{6}{5} =10} atop {frac{28}{5}-2 cdot (- frac{6}{5} )=8 }} right. \ \
left { {{frac{56}{5}- frac{6}{5} =10} atop {frac{28}{5}+ frac{12}{5} =8 }} right. \ \
left { {{frac{50}{5} =10} atop {frac{40}{5} =8 }} right. \ \
left { {{10 =10} atop {8 =8 }} right. \ \](https://tex.z-dn.net/?f=+left+%7B+%7B%7B2cdot+frac%7B28%7D%7B5%7D-+frac%7B6%7D%7B5%7D+%3D10%7D+atop+%7Bfrac%7B28%7D%7B5%7D-2+cdot+%28-+frac%7B6%7D%7B5%7D+%29%3D8+%7D%7D+right.+%5C+%5C%0A%0A+left+%7B+%7B%7Bfrac%7B56%7D%7B5%7D-+frac%7B6%7D%7B5%7D+%3D10%7D+atop+%7Bfrac%7B28%7D%7B5%7D%2B+frac%7B12%7D%7B5%7D+%3D8+%7D%7D+right.+%5C+%5C%0A%0A+left+%7B+%7B%7Bfrac%7B50%7D%7B5%7D+%3D10%7D+atop+%7Bfrac%7B40%7D%7B5%7D+%3D8+%7D%7D+right.+%5C+%5C%0A%0A+left+%7B+%7B%7B10+%3D10%7D+atop+%7B8+%3D8+%7D%7D+right.+%5C+%5C)
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