Question

ax + by = 1
bx + ay = 0 hallar x e y
​

Answer 1

Respuesta:

$x=\frac{a}{a^{2}+b^{2}}$

$y=-\frac{b}{a^{2}+b^{2}}$

Explicación paso a paso:

El sistema es:

$\left\lbrace\begin{array}{rcl}ax+by&=&1\\\\bx+ay&=&0\end{array}\right.$

Usando el método de Cramer

$\Delta=\left|\begin{matrix}a&b\\\\b&a\end{matrix}\right|=a^{2}-b^{2}$

$\Delta_{1}=\left|\begin{matrix}</p><p>1&b\\\\0&a\end{matrix}\right|=a$

$\Delta_{2}=\left|\begin{matrix}a&1\\\\b&0\end {matrix}\right|=-b$

$x=\frac{\Delta_{1}}{\Delta}=\frac{a}{a^{2}+b^{2}}$

$y=\frac{\Delta_{2}}{\Delta}=-\frac{b}{a^{2}+b^{2}}$

Por lo tanto las soluciones son:

$\left\lbrace\begin{array}{rcl}x&=&\frac{a}{a^{2}+b^{2}}\\\\y&=&-\frac {b}{a^{2}+b^{2}}\end{array}\right.$