$\left\{ \begin{array} { l } { 2 a x + b y = 14 } \\ { - 2 x + 9 y = - 19 } \end{array} \right.$

## 共享

2ax+by=14,-2x+9y=-19

2ax+by=14

2ax=\left(-b\right)y+14

x=\frac{1}{2a}\left(\left(-b\right)y+14\right)

x=\left(-\frac{b}{2a}\right)y+\frac{7}{a}

-2\left(\left(-\frac{b}{2a}\right)y+\frac{7}{a}\right)+9y=-19

\frac{b}{a}y-\frac{14}{a}+9y=-19

\left(\frac{b}{a}+9\right)y-\frac{14}{a}=-19

\left(\frac{b}{a}+9\right)y=-19+\frac{14}{a}

y=\frac{14-19a}{9a+b}

x=\left(-\frac{b}{2a}\right)\times \left(\frac{14-19a}{9a+b}\right)+\frac{7}{a}

x=-\frac{b\left(14-19a\right)}{2a\left(9a+b\right)}+\frac{7}{a}

x=\frac{19b+126}{2\left(9a+b\right)}

x=\frac{19b+126}{2\left(9a+b\right)},y=\frac{14-19a}{9a+b}

2ax+by=14,-2x+9y=-19

\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}14\\-19\end{matrix}\right)

inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2a\times 9-b\left(-2\right)}&-\frac{b}{2a\times 9-b\left(-2\right)}\\-\frac{-2}{2a\times 9-b\left(-2\right)}&\frac{2a}{2a\times 9-b\left(-2\right)}\end{matrix}\right)\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2\left(9a+b\right)}&-\frac{b}{2\left(9a+b\right)}\\\frac{1}{9a+b}&\frac{a}{9a+b}\end{matrix}\right)\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2\left(9a+b\right)}\times 14+\left(-\frac{b}{2\left(9a+b\right)}\right)\left(-19\right)\\\frac{1}{9a+b}\times 14+\frac{a}{9a+b}\left(-19\right)\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{19b+126}{2\left(9a+b\right)}\\\frac{14-19a}{9a+b}\end{matrix}\right)

x=\frac{19b+126}{2\left(9a+b\right)},y=\frac{14-19a}{9a+b}

2ax+by=14,-2x+9y=-19

-2\times 2ax-2by=-2\times 14,2a\left(-2\right)x+2a\times 9y=2a\left(-19\right)

\left(-4a\right)x+\left(-2b\right)y=-28,\left(-4a\right)x+18ay=-38a

\left(-4a\right)x+4ax+\left(-2b\right)y+\left(-18a\right)y=-28+38a

\left(-2b\right)y+\left(-18a\right)y=-28+38a

\left(-18a-2b\right)y=-28+38a

\left(-18a-2b\right)y=38a-28

y=-\frac{19a-14}{9a+b}

-2x+9\left(-\frac{19a-14}{9a+b}\right)=-19

-2x-\frac{9\left(19a-14\right)}{9a+b}=-19

-2x=-\frac{19b+126}{9a+b}

x=\frac{19b+126}{2\left(9a+b\right)}

x=\frac{19b+126}{2\left(9a+b\right)},y=-\frac{19a-14}{9a+b}

2ax+by=14,-2x+9y=-19

2ax+by=14

2ax=\left(-b\right)y+14

x=\frac{1}{2a}\left(\left(-b\right)y+14\right)

x=\left(-\frac{b}{2a}\right)y+\frac{7}{a}

-2\left(\left(-\frac{b}{2a}\right)y+\frac{7}{a}\right)+9y=-19

\frac{b}{a}y-\frac{14}{a}+9y=-19

\left(\frac{b}{a}+9\right)y-\frac{14}{a}=-19

\left(\frac{b}{a}+9\right)y=-19+\frac{14}{a}

y=\frac{14-19a}{9a+b}

x=\left(-\frac{b}{2a}\right)\times \left(\frac{14-19a}{9a+b}\right)+\frac{7}{a}

x=-\frac{b\left(14-19a\right)}{2a\left(9a+b\right)}+\frac{7}{a}

x=\frac{19b+126}{2\left(9a+b\right)}

x=\frac{19b+126}{2\left(9a+b\right)},y=\frac{14-19a}{9a+b}

2ax+by=14,-2x+9y=-19

\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}14\\-19\end{matrix}\right)

inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2a&b\\-2&9\end{matrix}\right))\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2a\times 9-b\left(-2\right)}&-\frac{b}{2a\times 9-b\left(-2\right)}\\-\frac{-2}{2a\times 9-b\left(-2\right)}&\frac{2a}{2a\times 9-b\left(-2\right)}\end{matrix}\right)\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2\left(9a+b\right)}&-\frac{b}{2\left(9a+b\right)}\\\frac{1}{9a+b}&\frac{a}{9a+b}\end{matrix}\right)\left(\begin{matrix}14\\-19\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{9}{2\left(9a+b\right)}\times 14+\left(-\frac{b}{2\left(9a+b\right)}\right)\left(-19\right)\\\frac{1}{9a+b}\times 14+\frac{a}{9a+b}\left(-19\right)\end{matrix}\right)

\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{19b+126}{2\left(9a+b\right)}\\\frac{14-19a}{9a+b}\end{matrix}\right)

x=\frac{19b+126}{2\left(9a+b\right)},y=\frac{14-19a}{9a+b}

2ax+by=14,-2x+9y=-19

-2\times 2ax-2by=-2\times 14,2a\left(-2\right)x+2a\times 9y=2a\left(-19\right)

\left(-4a\right)x+\left(-2b\right)y=-28,\left(-4a\right)x+18ay=-38a

\left(-4a\right)x+4ax+\left(-2b\right)y+\left(-18a\right)y=-28+38a

\left(-2b\right)y+\left(-18a\right)y=-28+38a

\left(-18a-2b\right)y=-28+38a

\left(-18a-2b\right)y=38a-28

y=-\frac{19a-14}{9a+b}

-2x+9\left(-\frac{19a-14}{9a+b}\right)=-19

-2x-\frac{9\left(19a-14\right)}{9a+b}=-19

-2x=-\frac{19b+126}{9a+b}

x=\frac{19b+126}{2\left(9a+b\right)}

x=\frac{19b+126}{2\left(9a+b\right)},y=-\frac{19a-14}{9a+b}