Question

b) 12X - Y = 287 3X + 2Y= 101
metodo de igualacion​

Answer 1

Respuesta:

$x=\frac{157}{97},\:y=-\frac{832}{97}$

Explicación paso a paso:

$\begin{bmatrix}12x-y=28\\ 73x+2y=101\end{bmatrix}\\\\12x-y=28\\\\12x-y+y=28+y\\\\12x=28+y\\\\\frac{12x}{12}=\frac{28}{12}+\frac{y}{12}\\\\x=\frac{28+y}{12}\\\\\begin{bmatrix}73\cdot \frac{28+y}{12}+2y=101\end{bmatrix}\\\\\\=\frac{73\left(y+28\right)}{12}+2y\\\\=\frac{\left(28+y\right)\cdot \:73}{12}+\frac{2y\cdot \:12}{12}\\\\=\frac{\left(28+y\right)\cdot \:73+2y\cdot \:12}{12}\\\\=\frac{2044+97y}{12}\\\\\frac{2044+97y}{12}=101$

$\begin{bmatrix}\frac{2044+97y}{12}=101\end{bmatrix}\\\\x=\frac{28-\frac{832}{97}}{12}\\\\\frac{28-\frac{832}{97}}{12}\\\\=\frac{\frac{1884}{97}}{12}\\\\=\frac{1884}{97\cdot \:12}\\\\=\frac{1884}{1164}\\\\=\frac{157}{97}\\\\x=\frac{157}{97}\\\\x=\frac{157}{97},\:y=-\frac{832}{97}$