3.1 Yhtälöryhmä

3.1 Yhtälöryhmä https://peda.net/id/923eea38722 2019-05-09T09:20:41+03:00 https://peda.net/:static/537/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> 309 https://peda.net/id/181e872872e 2019-05-10T08:25:59+03:00 a) ei voida<br/> b) kyllä, r=-3 2019-05-10T08:25:59+03:00 302 https://peda.net/id/9d5ae48c722 2019-05-09T09:42:29+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0Ax%2By%2B2z%3D7%26%5Cleft(1%5Cright)%5C%5C%0A-x-y%2Bz%3D2%26%5Cleft(2%5Cright)%5C%5C%0A2x%2By%2Bz%3D6%26%5Cleft(3%5Cright)%0A%5Cend%7Bcases%7D" alt="\begin{cases}
x+y+2z=7&\left(1\right)\\
-x-y+z=2&\left(2\right)\\
2x+y+z=6&\left(3\right)
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%2B%5Cbegin%7Bcases%7D%0Ax%2By%2B2z%3D7%26%5C%5C%0A-x-y%2Bz%3D2%26%0A%5Cend%7Bcases%7D" alt="+\begin{cases}
x+y+2z=7&\\
-x-y+z=2&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=--------------" alt="--------------"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3z%3D9%5C%20%5Cparallel%3A3" alt="3z=9\ \parallel:3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=z%3D3" alt="z=3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%2B%5Cbegin%7Bcases%7D%0A-x-y%2B3%3D2%26%5C%5C%0A2x%2By%2B3%3D6%26%0A%5Cend%7Bcases%7D" alt="+\begin{cases}
-x-y+3=2&\\
2x+y+3=6&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=--------------" alt="--------------"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2" alt="x=2"/></div> <div>sijoitetaan x ja z johonkin ja ratkaistaan y</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=-x-y%2Bz%3D2" alt="-x-y+z=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-2-y%2B3%3D2" alt="-2-y+3=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-y%3D1" alt="-y=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D-1" alt="y=-1"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0Ax%3D2%26%5C%5C%0Ay%3D-1%26%5C%5C%0Az%3D3%26%0A%5Cend%7Bcases%7D" alt="\begin{cases}
x=2&\\
y=-1&\\
z=3&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=tarkistetaan" alt="tarkistetaan"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0A2-1%2B6%3D7%26T%5C%5C%0A-2%2B1%2B3%3D2%26T%5C%5C%0A4-1%2B3%3D6%26T%0A%5Cend%7Bcases%7D" alt="\begin{cases}
2-1+6=7&T\\
-2+1+3=2&T\\
4-1+3=6&T
\end{cases}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0A2x%2By%2Bz%3D4%26%5Cleft(1%5Cright)%5C%5C%0Ax%2B2y%2B3z%3D8%26%5Cleft(2%5Cright)%5C%5C%0A3x%2B2y%2Bz%3D4%26%5Cleft(3%5Cright)%0A%5Cend%7Bcases%7D" alt="\begin{cases}
2x+y+z=4&\left(1\right)\\
x+2y+3z=8&\left(2\right)\\
3x+2y+z=4&\left(3\right)
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0A2x%2By%2Bz%3D4%26%5C%5C%0Ax%2B2y%2B3z%3D8%26%5Cparallel%5Ccdot%5Cleft(-2%5Cright)%0A%5Cend%7Bcases%7D" alt="\begin{cases}
2x+y+z=4&\\
x+2y+3z=8&\parallel\cdot\left(-2\right)
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%2B%5Cbegin%7Bcases%7D%0A2x%2By%2Bz%3D4%26%5C%5C%0A-2x-4y-6z%3D-16%26%0A%5Cend%7Bcases%7D" alt="+\begin{cases}
2x+y+z=4&\\
-2x-4y-6z=-16&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-------------" alt="-------------"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3y-5z%3D-12" alt="-3y-5z=-12"/><br/> <div><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0Ax%2B2y%2B3z%3D8%26%5Cparallel%5Ccdot%5Cleft(-3%5Cright)%5C%5C%0A3x%2B2y%2Bz%3D4%26%0A%5Cend%7Bcases%7D" alt="\begin{cases}
x+2y+3z=8&\parallel\cdot\left(-3\right)\\
3x+2y+z=4&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%2B%5Cbegin%7Bcases%7D%0A-3x-6y-9z%3D-24%26%5C%5C%0A3x%2B2y%2Bz%3D4%26%0A%5Cend%7Bcases%7D" alt="+\begin{cases}
-3x-6y-9z=-24&\\
3x+2y+z=4&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-------------" alt="-------------"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-4y-8z%3D-20" alt="-4y-8z=-20"/></div> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0A-3y-5z%3D-12%26%5Cparallel%5Ccdot%5Cleft(-4%5Cright)%5C%5C%0A-4y-8z%3D-20%26%5Cparallel%5Ccdot3%0A%5Cend%7Bcases%7D" alt="\begin{cases}
-3y-5z=-12&\parallel\cdot\left(-4\right)\\
-4y-8z=-20&\parallel\cdot3
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0A12y%2B20z%3D48%26%5C%5C%0A-12y-24z%3D-60%26%0A%5Cend%7Bcases%7D" alt="\begin{cases}
12y+20z=48&\\
-12y-24z=-60&
\end{cases}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-4z%3D-12%5C%20%5Cparallel%3A%5Cleft(-4%5Cright)" alt="-4z=-12\ \parallel:\left(-4\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=z%3D3" alt="z=3"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=-3y-5%5Ccdot3%3D-12" alt="-3y-5\cdot3=-12"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3y%3D3" alt="-3y=3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D-1" alt="y=-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%2By%2Bz%3D4" alt="2x+y+z=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x-1%2B3%3D4" alt="2x-1+3=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%3D2" alt="2x=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Bcases%7D%0A2-1%2B3%3D4%26T%5C%5C%0A1-2%2B9%3D8%26T%5C%5C%0A3-2%2B3%3D4%26T%0A%5Cend%7Bcases%7D" alt="\begin{cases}
2-1+3=4&T\\
1-2+9=8&T\\
3-2+3=4&T
\end{cases}"/></div> </div> 2019-05-09T09:42:29+03:00 301 https://peda.net/id/ca412572722 2019-05-09T09:22:15+03:00 Yhtälöryhmän oikea ratkaisu on II x=-1, y=1 ja z=2 2019-05-09T09:22:15+03:00